Slide 1

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 2

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 3

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 4

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 5

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 6

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 7

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 8

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 9

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 10

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 11

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 12

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 13

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 14

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 15

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 16

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 17

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 18

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 19

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 20

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 21

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 22

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 23

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 24

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?


Slide 25

Quantum Theory and the
Atom
Chapter 5
Section 2

Bohr Model of the Atom
 Observed: hydrogen only emits certain
frequencies of light
 Niels Bohr (Danish) proposed a quantum
model for the atom:
– Lowest energy level allowed for an electron is
its ‘ground state’
– When atom gains energy, electron goes to a
higher level, an ‘excited state’.
– The electron can have many ‘excited’ states

Bohr Model (Cont.)
– Each energy level corresponds to one
quanta of energy

 Bohr model correctly predicted the
emission spectra for hydrogen.

Bohr Atomic Model

Explaining the Hydrogen Line
Spectrum
 When energy is added, electron moves to a
higher-energy orbit (from n = 1 to n = 2)
 When atom moves back to lower-energy
orbit, a ‘photon’ of energy is released
 Energy release is equal to the frequency of
the light spectrum.
 Because only certain atomic energies are
possible (certain orbits), only specific
frequencies are emitted.

Energy and Atoms
 Higher Energy Orbit

Lower Energy Orbit

– Specific distance
– Specific amount of energy (quanta)
– Specific frequency
– Specific frequency = specific color

Bohr Atomic Model
 Bohr model failed to explain the spectra of
any other element
 It was later determined that the Bohr model
was fundamentally correct.

Quantum Mechanical Model
 1920’s – DeBroglie (French) Experiments
 Electron orbits behaved like waves, could
they have multiple frequencies?
 Could particles, including electrons, behave
like waves?
 If an electron has a wavelike motion AND is
restricted to circular orbits of fixed radius,
the electron is allowed only certain
wavelengths

Multiples of Wavelengths

Wavelengths in Orbits

Quantum Mechanical Model
 DeBroglie Equation
–  = h/mv

 Predicts that ALL moving particles have
wave characteristics
– Auto moving at 25 m/s, with mass 910kg has a
wavelength of 2.9x10-38 (way too small to be
detected)
– Electron at same speed has a wavelength of
2.9x10-5 (easily measured)

DeBroglie’s Findings
 Notice also that this
means the electron
does not exist at one
single spot in its
orbit, it has a wave
nature and exists at
all places in the
allowed orbit. And
the Bohr atom really
looks like the
following diagram:

Heisenberg Uncertainty Principle
 It is impossible to make any measurement
on an object without disturbing the object at
least a little;
 States:
– That is is fundamentally impossible to know
precisely both the velocity and the position of a
particle at the same time.

Heisenberg Uncertainty Principle

Schrödinger Wave Equation
 1926 Erwin Schrödinger (Austria) furthered
the theory.
– Created an equation that treated the hydrogen
atom’s electron like a wave
– New model applied equally well to other atoms

 This body of knowledge became the
“quantum mechanical model of the atom”

Just For Reference…
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is
also often called the Schrödinger wave equation, and is a partial differential equation that describes how the
wavefunction of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the
Schrödinger equation is sometimes known as the Schrödinger picture, as distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg picture. The time-dependent one-dimensional Schrödinger equation is
given by

where i is the imaginary unit,

is the time-dependent wavefunction,

is h-bar, V(x) is the potential,

and
is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts
using separation of variables
to write (
2
)

thus obtaining

(
3
)

Setting each part equal to a constant then gives

And so on and so on…..
(
6
)

What does this mean about
electron orbits?
 Atomic orbits are 3-dimensional regions
around the nucleus (like a fuzzy cloud).
 Principal quantum numbers are assigned to
indicate relative size and energy of orbitals
– As n increases, orbital gets larger, has more
energy;
– Up to 7 energy levels have been detected for
hydrogen

What does this mean about
electron orbits?
 Each principal energy level can have
sublevels
– Principal energy level one has only one
sublevel
– Principal energy level 2 has 2 sublevels
– Principal energy level 3 has 3 sublevels
– And so on..

What does this mean about
electron orbits?
 Sublevels are labeled s, p, d, or f according to
their shape
– s sublevels are spherical
– p sublevels are dumbell shaped
– d sublevels and f sublevels are not all shaped
the same.

 Each orbital can have at most 2 electrons

What does this mean about
electron orbits?
 Principal level one has only ONE sublevel
– Designated as 1s (spherical)
– 2 total electrons (2 elements in 1st row)

 Principal level 2 has 2 sublevels
– Designated as 2s and 2p
– 2s is spherical (like 1s) but larger
– 2p has three dumbbell shaped orbitals on each
of three axis
– Total 8 electrons (8 elements)

What does this mean about
electron orbits?

What does this mean about
electron orbits?

What does this mean about
electron orbits?

Note alignment along
the axes

What does this mean about
electron orbits?
 Third principal energy level has 3 sublevels:
– 3s, 3p, and 3d
– d-orbitals have 5 orbitals of equal energy
– 4 of the d-orbitals have identical shapes but
different orientations
– 5th d-orbital has a different shape and
orientation than the others

What does this mean about
electron orbits?