Transcript Chapter 6 Electronic Structure of Atoms
CHM 1045: General Chemistry and Qualitative Analysis
Unit 7 Electronic Structure of Atoms
Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL
Textbook Reference:
•
Module #9
Electronic Structure of Atoms
Atoms and Electromagnetic Radiation
Atoms absorb and emit energy
, often in the form of electromagnetic radiation (visible light, microwaves, radio & TV waves, u.v., infrared,etc) Electronic Structure of Atoms {Fireworks}
The Nature of Light Energy
(1) White Light is not white, it is colored: the Spectrum:
Spectroscope
(2) Light is electrical and magnetic (electromagnetic) (3) Light does not travel in truly straight lines, it travels in waves {3D-Wave}
V
I
B G.Y O R
i o l e t
n d i g
l u e r e e n e l l o w r a n g e e d
Electronic Structure of Atoms o
Light Energy as Waves
:
two important characteristics short = high
1. wavelength (
) :
the distance (m) between corresponding points on adjacent waves long = low
2. frequency (
)
or
(
f
) :
the number of waves passing a given point per unit of time (1/s = s
1-
) !
For waves traveling at the same velocity,
the longer the wavelength, the smaller the frequency
Knowing and
,
you calculate the
speed of light
c
1
constant (c) (m) (1/sec) SPEED = DISTANCE x PER UNIT TIME Speed (c) = wave length ( λ) x frequency ( Electronic ) of Atoms m/sec = m x 1/sec
Electromagnetic Radiation
A form of energy characterized by waves (or pulses) of varying frequencies
( )
and wavelengths
( ) .
c
c
{*Light Waves} {3D-Wave} {Wavelength of v. l.} Electronic Structure of Atoms
Electromagnetic Radiation
• Speed of Light: All electromagnetic radiation travels at the same velocity (
c
), 3.00 10 8 m/s.
Einstein’s Theory of Special Relativity: Energy and mass are different forms of the same thing α 1 E m c 2 c Frequency (
f
) Problem: What is the wavelength of a photon of light that has a frequency of 3.8 x 10 9 c c s -1 ?
3 .
00 x 10 8 m s -1 3.8
x 10 9 s 1 = 7.89x10
-2 m Structure of Atoms
The Nature of Energy: Discrete vs. Continuous
Digital: 0110100101001 Analog Eggs: Quanta (Photon): particles Waves: Water:
Electronic Structure of Atoms
Energy as a Particle
Light Energy When light energy shines on a metal, an electron current is generated.
(Photon, Quanta)
waves particles {
Photoelectric Effect
} Light is behaving as a
particle
( photon ) that knocks-off valence electrons from the metal.
Electronic Structure of Atoms
Energy as a Particle (Photon, Quanta)
{Metals & EM Radiation} • The wave nature of light does not explain how an object can glow when its temperature increases.
• Max Planck explained it by assuming that energy comes in packets called
quanta
(energy bundle, photon).
Max Planck
(1848-1947)
Planck
concluded that
energy
(
E
) is proportional to
frequency
(): E h For any particular
frequency
( ) there is a particular bundle of
Energy
(E) that exists as a discrete quantity (quanta) that is a multiple of
Planck’s constant
(
h
).
where
h
is
Planck’s constant
, 6.63 10 −34 J-s. Energy from electrons comes in discrete are
whole number multiples of h
.
quantities (bundles)
1 2 that Structure of Atoms
The Nature of Energy
Since
c =
,
then
c
E
h
h
c
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light.
Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10 -14 erg? {Note: Modules use erg =10 -7 Joule} Electronic Structure of Atoms
The Nature of Energy
E
=
h
h
c
Problem : What is the wavelength (in Å) of a ray whose energy is 6.16 x 10 -21 Joules? {Note: Modules use erg =10 -7 Joule}
h
c E
6 .
63 x 10 34 Joules.sec
3 .
0 x 10 6 .
16 x 10 8
m
21 / sec
Joules
3.23
x 10 -5
m
?
Å
3.23
x 10 -5
m
10 1 Å 10
m
3 .
23 x 10 5 Å
Electronic Structure of Atoms
Electronic Structure of Atoms
Energy as……
(1) Waves
c =
c
(2) Particle (Photon, Quanta) (3) Matter
ΔE
=h
E m c 2
E
h
h
c
Electronic Structure of Atoms
• •
The Wave-Particle Duality of Matter
Electromagnetic radiation can behave as a particle or as wave phenomena {ElectonWaves}
Louis de Broglie
posited that
if light can have material properties, matter should exhibit wave properties.
• He demonstrated that the relationship between mass ( m ) and wavelength ( ) was: ∝ 1
m
=
h m v
velocity (v) (where
h
is Planck’s constant, 6.63 10 −34 of light) J-s, and v Electronic is velocity Structure of Atoms = eq given
The Wave Nature of Matter
Problem: An electron has a mass of 9.06 x 10 -25 kg and is traveling at the speed of light. Calculate its wavelength?
=
h mv
( 6 .
63 x 10 -34
J
/
s
) ( 9.06
x 10 25 kg ) x (3.00
x 10 8 m/s) 2.44
x10 18 m Problem: What is the wavelength of a 70.0 kg skier traveling down a mountain at 15.0 m/s?
=
h mv
( 6 .
63 x 10 -34
J
/
s
) ( 70 .
0
kg
) x (15.0
m/s)
6.31
x10 37 m
Electronic Structure of Atoms J = Joule = kg
.
m 2
The Nature of Energy
White Light’s Continuous Spectrum:
V
I
B G.Y O R
Electronic Structure of Atoms
The Nature of Energy
Substances both absorb and emit only certain Discrete Spectra {Flame Tests.Li,Na,K} {Na,B} {AtomicSpectra} Electronic Structure of Atoms
•
The Bohr “Planetary” Model of the Atom
(1913)
Niels Bohr adopted Planck’s assumption and explained atomic phenomena in this way: 1.
2.
Electrons in an atom can only occupy certain orbits (corresponding to certain energies, frequencies and wavelengths, because
E=h
=h c/
λ
).
Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
1 st EL f = 4 2 nd EL f = 5
3.
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E
=
h
Electronic Structure of Atoms
The Bohr Model of the Atom
Which series releases most energy?
{ExcitedElectrons*} Electronic Structure
greater the energy
Atomic Spectra & Bohr Atom
The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the Rydberg formula for hydrogen (1885)
1
R H
( )
n f 2
-
n
1
i 2
Rydberg formula for hydrogen-like elements ( He + , Li 2+ , Be 3+ etc., ) 1 where
R H
is the and
n i
and
n f
of the electron. Z Rydberg constant, 2.18 is the atomic number 10 −18 of Atoms J,
Atomic Spectra & Bohr Atom
Since energy and wavelength are mathematically related, the Rydberg Equation can also be expressed in terms of energy:
1
E
E
=
R H 2.180
( )
n f 2
n f x 10 -18
J
n i
-
=
n f 2
-
R n i H 2 2.180
x 10 -18
J n i 2
E f
E i
The energy possessed by an electron at a particular energy level (E n ) can be expressed as:
E
n
2.180
x 10
-18
n 2 Joule where
R H
is the Rydberg constant, 2.18 and final energy levels of the electron.
10 −18 J, and
n i
and
n f
= eq given Structure are the initial
Atomic Spectra and the Bohr Atom
Problem: How much energy (J) is liberated when an electron changes from n = 4 to n = 2? What is the wavelength (m) of the light emitted?
E E f E i 2.180
x 10 -18
J n
2
f
2.180
x 10 -18
J n i
2 2.180
x 10 -18 J 2 2 f 2.180
x 10 -18 J 4 i 2 E (0.545
x 10 -18 J) (0.1362
x 10 -18 J) 0 .
4088
x
10 -18
J
To convert energy to wavelength, we must employ the equations: c c E h
h
c
h
c E
6 .
63 x 10 34 J.s
3 .
0 x 10 8 m / s 0 .
4088 x 10 18 J 4.865
x 10 of Atoms
Atomic Spectra and the Bohr Atom
Notice that the wavelength calculated from the Rydberg equation matches the wavelength of the green colored line in the H spectrum. 4.865
x 10 -7 m E 0 .
4088 x 10 -18 J Electronic Structure of Atoms
2006 (B) Ele 1 Ele 2 Electronic Structure of Atoms
Heisenberg’s Uncertainty Principle
• Heisenberg showed that the more precisely the
momentum
of a particle is known, the less precisely is its
position
known: (
x
) (
mv
) 4
h
• In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!
Electronic Structure of Atoms
Quantum Model of the Atom
• Max Planck (energy quanta, Planck’s constant) • Albert Einstein (energy and frequency) • Niels Bohr (electrons and Spectra) • Louis de Broglie (particle-wave duality of matter) • Werner Heisenberg (electron uncertainty) • Erwin Schrödinger (probability wave function, the four
quantum numbers
) Prof. Alonso • Jörge L. Alôns ø (diagrammatic quantum mechanical atomic model) Solvay Conference in Brussels 1911 Electronic Structure of Atoms
Levels
= 1, 2, 3, etc
3d xy 3 Orbital
cloud
3d x 2 orientation
(x, y, z, etc)
3p z 2p z 3s 2s 3d yz 2p x 3p x 2
Sublevel
Orbital types
= s, p, d, f
3d xz 1s 2p y 3p y 3d x 2 y 2 4 spin
of Atoms cloud (2e- ea)
Levels
= 1, 2, 3, etc
3d xy 3 Orbital
cloud
3d x 2 orientation
(x, y, z, etc)
3p z 2p z 3s 2s 3d yz 2p x 3p x 2
Sublevel
Orbital types
= s, p, d, f
3d xz 1s 2p y 3p y 3d x 2 y 2 4 spin
of Atoms cloud (2e- ea)
Quantum Numbers
• Describe the location of electrons within atoms.
• There are four quantum numbers:
Principal
= describes the
energy level
(1,2,3,etc)
Azimuthal
d 10 , f 14 ) = energy sublevel,
orbital type
(s 2 , p 6 ,
Magnetic
=
orbital orientation
or cloud (2 electrons on each cloud) Example: three p clouds: p x , p y , p z
Spin
= which way the electron is spinning (↑↓) Electronic Structure of Atoms
Electron Configuration
,
Orbital Notation
and Quantum Numbers
Principal
(n)=
energy level
Azimuzal
( ) =
sublevel orbital type
1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4 s 2 4 p 6 4 d 10 4 f 14
Magnetic
(
m l
) =
orbital cloud orientation
(2e per orbital)
Spin
(
m s
) = electron + or Electronic Structure of Atoms
Electron Configuration
Two issues: (1)Arrangement of electrons within an atom 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 14 (2) Order in which electrons fill the orbitals 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 Aufbau Process: Using Periodic Table Sub-blocks: Electronic Structure of Atoms
Historic Development of Atomic Theory
Bohr (1913) Schrödinger (1926) Electronic Structure of Atoms
The Schrödinger Equation
t
i • is the imaginary unit , ( complex number number) whose square is a negative real • is time, • is the partial derivative with respect to
t
, • is the reduced Planck's constant (Planck's constant divided by 2π), ψ(
t
) • ψ(
t
) is the wave function , • is the Hamiltonian space ).
(a self-adjoint operator acting on the Electronic state of Atoms
Quantum Mechanics
• Developed by Erwin Schrödinger, it is a
mathematical model
incorporating both the wave & particle nature of electrons.
• The
wave function
is designated with a lower case Greek
psi
( ).
• The square of the wave function,
2
, gives a
probability density
map of where an electron has a certain statistical likelihood of being at any given instant in time.
Electronic Structure
The Schrödinger Equation
• Solving the wave equation gives a set of wave functions , or
orbitals
, and their corresponding energies.
• Each orbital describes a
spatial distribution of electron density
.
• An orbital is described by a set of three quantum numbers .
Electronic Structure of Atoms
Principal Quantum Number , n
1 2 3
• The principal quantum number,
n
, describes the
energy level
on which the orbital resides.
• The values of
n
are integers ≥ 0. Electronic Structure of Atoms
Azimuthal Quantum Number
,
• This quantum number defines the
shape of the orbital
.
• Allowed values of are integers ranging from 0 to
n
− 1.
• We also use letter designations: Value of 0 1 2 3 Type of orbital
= 0
= 1
s p
= 2
d f
= 3
Electronic Structure of Atoms
Magnetic Quantum Number , m
l
• Describes the
three-dimensional orientation of the orbital.
• Values are integers ranging from -
l
to
l
: −
l
≤
m l
≤
l.
• Therefore, on any given energy level, there can be up to 1
s
orbital, 3
p
orbitals, 5
d
orbitals, 7
f
orbitals, etc.
0 +1 0
Electronic Structure
-1
of Atoms
Values of Quantum Numbers
• • •
Principal Quantum #: values of
n
are integers ≥ 0 . Azimuthal Quantum #: values of
are integers ranging from 0 to n − 1 .
Magnetic Quantum #: values are integers ranging from -
to
: −
≤
m l
≤
.
Electronic Structure of Atoms
s
Orbitals (
= 0)
Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that
s
orbitals possess
n
−1 nodes , or regions where there is 0 probability of finding an electron.
Electronic Structure
s
Orbitals (
= 0)
• Spherical in shape.
• Radius of sphere increases with increasing value of
n.
{1s} {2s} {3s} Electronic Structure of Atoms
p
Orbitals (
= 1)
• Have two lobes with a node between them.
+1
{p x }
0
{p y }
-1
{p z } Electronic Structure {www.link}
Orbital Overlap: 1s
2
2s
2
2p
6
1s 2s
+
2p “P” orbital electrons are repelled time nucleus.
by the “S” orbital electrons and so spend more further from the “P” orbital electrons also repel from each others’ sublevels, so they run along
Structure
the axes.
of Atoms
-1 1
d
Orbitals (
= 2)
2 0 -2
•Four of the five orbitals have 4 lobes; the other resembles a the center.
p
orbital with a doughnut around Electronic Structure {*Orbitals.s.p.d} of Atoms {www.link}
3 2 1 -1 0
f
Orbitals (
= 3)
-2 -3
• There are seven f orbitals per n level.
The f orbitals have complicated names.
They have an = 3 m = -3,-2,-1,0,+1,+2, +3 7 values of m The f orbitals have important effects in the lanthanide and actinide elements.
Electronic Structure of Atoms {www.link.f}
Energies of Orbitals
• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
• That is, they are degenerate (collapsed).
Electronic Structure of Atoms
Energies of Orbitals
• As the number of electrons increases, though, so does the repulsion between them.
• Therefore, in many electron atoms, orbitals on the same energy level are no {E.L. vs FillingOrder} longer degenerate .
Electronic Structure of Atoms
Electron Configuration & Periodic Table
Electronic Structure of Atoms
Spin Quantum Number ,
m s
• 1920s: it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which Structure energy.
{e-spin}
Electron Configurations
• Distribution of all electrons in an atom.
• Consist of Number denoting the energy level.
Letter denoting the type of orbital.
Superscript denoting the number of electrons in those orbitals.
Electronic Structure of Atoms
Orbital Diagrams
• Each box represents one orbital.
• Half-arrows represent the electrons.
• The direction of the arrow represents the spin of the electron.
Electronic Structure of Atoms
Basic Principles of Electron Configuration Notations
• • •
Pauli Exclusion Principle Hund’s Rule
of Maximum Multiplicity
Alonso’s Rules
of the Stability of Degenerate Orbitals Electronic Structure of Atoms
Pauli Exclusion Principle
Only two electrons can occupy an orbital and they must have opposite spins.
energy (identical sets of quantum numbers) Structure of Atoms
Hund’s Rule
of Maximum Multiplicity
One electron fills each orbital before a second of opposite spin accompanies it.
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” {Electron Configuration} {Electron Configuration2} Electronic Structure of Atoms
Alonso’s Rules
of the Stability of Degenerate Orbitals
s d
Completely Filled Completely Filled Completely Filled Half Filled
Most Stable Electron Configuration
Half Filled Half Filled Completely Filled Not even Half Filled Phenomenon also occurs between degenerate s and f orbitals Electronic Structure of Atoms
Periodic Table and Electron Configuration
{e- filling order} Electronic Structure of Atoms
Electronic configuration :
Nitrogen
1s 2 2s 2 2p 3 4s 3s 3p 3d 2p 2s 1s Hund’s Rule 1 1 2 GROUP
3 4 5 6 7 0
2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Neon
4s Electronic configuration: 3d 3p 3s 2p 2s 1s 1s 2 2s 2 2p 6 Hund’s Rule 1 1 2 GROUP
3 4 5 6 7 0
2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Vanadium
4s Electronic configuration: 3p 3d [Ar] 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 3s 2p 2s 1s [Ne] 1 1 2 GROUP
3 4 5 6 7 0
2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Chromium
4s 3s Electronic configuration: 3p 2p 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 3d [Ar] [Ne] Notice that one of the 4s electrons has been transferred to 3d so that 3d is now a
half filled
shell with extra stability. 4s and 3d contain only unpaired electrons.
2s 1 1 2 GROUP
3 4 5 6 7 0
1s 2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Nickel
4s Electronic configuration: 3p 3d [Ar] 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 8 3s 2p 2s 1s [Ne] 1 1 2 GROUP
3 4 5 6 7 0
2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Copper
4s Electronic configuration: 3d 3p 3s 2p 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 Notice that again one of the 4s electrons has been promoted to 3d so that 3d is now a
completely filled
shell with extra stability. 2s 1s 1 1 2 GROUP
3 4 5 6 7 0
2
3
4
Ti
Mn Fe Co
Zn Ga Ge As Se Br Kr Electronic Structure of Atoms
Some Anomalies
Some irregularities occur when there are enough Electronic electrons to half-fill
s
and
d
Structure orbitals on a given row.
Some Anomalies
Electron configuration for copper is [Ar] 4s 1 3d 5 rather than the expected [Ar] 4s 2 3d 4 .
•This occurs because the s and d Structure of Atoms
Some Anomalies
• These anomalies also occur in
f
-block atoms, as well. Electronic Structure of Atoms
Electron Configuration
Identify elements which posses the following electron configurations:
1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6
Fe
{Aufbau order of filling} 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 [Ar] 4s 2 3d 6
Fe Fe
{Energy level order} {Previous Nobel Gas Abbreviation} [Ar] 4s 0 3d 6
Fe 2+
{Cations formed by removal of outermost electrons}
Write Elect-Config for S 2 [Ne] 3s 2 3p 6
Electronic Structure of Atoms
Electronic Structure of Atoms
Periodic Table and Electron Configuration
{e- filling order} Electronic Structure of Atoms
1 2 3 4 5 6 7
Uses dots to represent Valence Electrons = those in outermost Energy Level Transition Metals Have additional electrons, but they are in an energy level that is lower than the valence electrons.
Electronic Structure of Atoms
Electronic Structure of Atoms
Electrons behave as waves (like standing waves above) and particles.
Electron position cannot be pinned down.
Electons don’t follow orbits , but rather orbitals
Electronic Structure
describe their paths.
The Energy of Electromagnetic Waves
Einstein
concluded that
energy frequency
(): E h (
E
) is proportional to where
h
is Planck’s constant, 6.63 10 −34 J-s. Electronic Energy from electrons comes in whole number multiples of
h
.
of Atoms = eq given
The Bohr Model of the Atom
(1913)
Electronic Structure of Atoms
The Nature of Energy
• One does not observe a continuous spectrum, as one gets from a white light source.
• Only a line spectrum of discrete wavelengths is observed.
Electronic Structure of Atoms
Electronic Structure of Atoms
Atoms and Electromagnetic Radiation
•To understand the electronic structure of atoms, one must understand the nature of waves.
Atoms absorb and emit energy
, often in the form of electromagnetic radiation (light, microwaves, radio & TV waves, u.v., infrared,etc) Electronic Structure of Atoms