Chapter 6 ELECTRONIC STRUCTURE OF ATOMS

Electronic Structure

Much of what we know about the energy of electrons and their arrangement around the nucleus of an atom comes from analysis of light emitted or absorbed by matter.

The Wave Nature of Light

The Electromagnetic Spectrum

c

= l . n <>

Electromagnetic Radiation

Relating frequency and wavelength c

= l . n

c =

l .

f

c = speed of light = 3.00 x 10 8 m/s n or f = frequency in cycle per second or Hertz l = wavelength in meters (1 nm = 1 x 10 -9 m) Note: As wavelength increases, frequency (& energy) will decrease.

Limitations of the Wave Model of Light

The prevailing laws of physics couldn’t explain:

1)Blackbody Radiation – emission of light from hot objects 2)Photoelectric Effect – emission of electrons from metal surfaces on which light strikes 3)Emission Spectra – emission of light from excited gas atoms *Couldn’t relate temperature , intensity, & wavelength of light

Max Planck 1900

1. Solved problem by stating energy can only be released or absorbed in discrete ‘chunks’ of some minimum size.

2. He named this smallest quantity of energy a ‘quantum’.

3. He said the minimum amount of energy that an object can gain or lose is related to its frequency.

E = h

.

f

E = Energy in Joules h = Planck’s Constant = 6.626 x 10 -34 Joule-second f = frequency in cycles per second or Hertz

Albert Einstein 1905

1. Used Planck’s Quantum Theory to explain the photoelectric effect.

2. Photoelectric Effect - light shining on a clean metal surface causes the surface to emit electrons if the light is of a certain minimum frequency . http://web2.uwindsor.ca/courses/physics/high_schools/2005/Photoelectric_effect/hist.html

3. He said light energy hitting a metal surface is not like a wave but like a stream of tiny energy packets called ‘photons’.

4. He said the energy of a photon can also be found by:

E = h * f

6. No matter the intensity, if the photons don’t have enough energy, no electrons are emitted.

Dual Nature of Light

Planck & Einstein are describing light as behaving like tiny particles of energy – just like matter is made of particles!

We theorize light has both a wave like and a particle like nature.

We refer to this as the DUAL NATURE OF LIGHT.

Bohr Model of the Atom

1)Ground State = when electrons are in the lowest energy state 2)Excited State – when electrons absorb energy & move to a higher energy state 3)Spectra – light energy given off when electrons return to lower energy states LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.

Recall

• • • Hot objects give off light. When the light from a light bulb passes through a prism, a RAINBOW or CONTINUOUS SPECTRUM forms.

Remember ROY G. BIV?

Red, Orange, Yellow, Green, Blue, Indigo, Violet

When the light from an element gas tube passes through a prism, only some colors are seen – called a BRIGHT-LINE SPECTRUM or LINE SPECTRA.

Gas Tube Hydrogen’s Bright Line Spectrum as viewed through a prism  Power Supply Hydrogen gas gives off pink light

Often Shown This Way

This site shows the Line Spectra of Various Elements http://jersey.uoregon.edu/elements/Elements.html

Johann Balmer

Showed that the wavelengths of the four visible lines of hydrogen fit the following formula:

1/

l

= (R

H

)( 1/n

1 2

- 1/n

2 2

)

Where R H R H = Rydberg Constant = 1.096776 x 10 7 m -1 n = energy level

(

n 2 bigger than n 1 )

Niels Bohr explains Hydrogen’s Line Specta

Bohr’s Postulates

1) Electrons must be in specific energy levels 2) An electron in an allowed energy state will not radiate energy & spiral into the nucleus 3) Energy is emitted or absorbed by electrons as they move from one allowed energy state to another.

4) The amount of energy: E = h

.

f

How much energy?

Bohr calculated the energy an electron possesses when in each energy state.

E = (-2.18 x 10 -18 J) (1/n 2 )

where n = 1, 2, 3, etc.

n is the energy level or principal quantum number Note that the values are negative. The energy is lowest (most negative) for n = 1.

When the electron is completely removed and an ion forms the energy = zero.

E = (-2.18 x 10

-18

J) (1/n

2

)

And the Energy Change?

D

E = (-2.18 x 10

-18

J) (1/n

f 2 -

1/n

i 2

)

Where the initial energy state = n

i

Where the final energy state = n

f

Dual Nature of Light & Matter!

1. Light has both particle (photon) & wavelike properties.

2. Louis de Broglie suggested that matter is the same – called the de Broglie’s hypothesis.

3. Matter has both particle like & wave like properties.

De Broglie’s Hypothesis

For matter waves:

l

= h / (m

.

v)

Where: l = wavelength (meters) m v = momentum m = mass (kg) v = velocity (m/s) h = 6.626 x 10 -34 Joule-second Recall: 1 Joule = 1 kg-m 2 /s 2 This wavelength only becomes significant when dealing with tiny high velocity particles such as electrons.

Heisenberg’s Uncertainty Principle

Heisenberg’s Uncertainty Principle: It is inherently impossible for us to know simultaneously both the exact momentum of an object and its exact location in space.

This becomes significant when dealing with the position of electrons within an atom.

QUANTUM MECHANICS

LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.

It took Quantum Mechanics to explain the behavior of light emitted by multi-electron atoms.

Quantum Mechanics is one of the most revolutionary discoveries of the 20 th century – the ‘new’ physics.

Quantum Mechanics

Heisenberg & de Broglie set the stage for a new model of the electron that would describe its location not precisely, but in terms of probabilities - called Quantum Mechanics or Wave Mechanics.

Erwin Schrodinger (1887 – 1961)

1) Proposed a Wave Equation (wave functions y ) that incorporates the dual nature of the electron.

2) Y 2 provides info about the electron’s location.

3) In the Quantum Mechanical Model, we speak of the probability ( Y 2 ) that the electron will be in a certain region of space at a given instant.

4) We call it probability density or electron density.

Con’t

4) The wave functions are called orbitals.

5) Orbitals differ in energy, shape, and size.

6) An orbital can hold up to TWO electrons.

7) Four numbers can be used to describe the location of an electron in an orbital.

Four Quantum Numbers

• • • • 1 st Quantum Number = The Principal Quantum Number (n) 2 nd Quantum Number = The Azimuthal Quantum Number or The Angular Momentum Quantum Number (

l

) 3 rd Quantum Number = The Magnetic Quantum Number (

m l

) 4 th Quantum Number = The Spin Magnetic Quantum Number (

m

s )

Pauli Exclusion Principle

Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n,

l

,

m l

,

m

s )

1

st

Quantum Number

It tells the principal energy level (shell) – ‘n’ n = 1 for the 1st PEL n = 2 for the 2 nd PEL , etc.

As the value of ‘n’ increases, the electron has more energy, is less tightly bound to the nucleus, and it spends more time further away from the nucleus.

2

nd

Quantum Number

It tells the sublevel or subshell, which indicates the shape of the orbital – ‘

l

’ If ‘

l

’ = zero, the sublevel is s If ‘

l

’ = 1, the sublevel is p If ‘

l

’ = 2, the sublevel is d If ‘

l

’ = 3, the sublevel is f In terms of energy, s < p < d < f.

The value of ‘

l

’ is always at least one less than the value of ‘n’.

3 rd Quantum Number

It tells the orientation of the orbital in the sublevel -

m l

For the s sublevel, there is only one orientation:

m l

= 0 For the p sublevel, there are 3 possible orientations:

m l

= +1, 0, -1 For the d sublevel, there are 5 possible orientations:

m l

= +2, +1, 0, -1, -2 For the f sublevel, there are 7 possible orientations:

m l

= +3, +2, +1, 0, -1, -2, -3

4th Quantum Number

It tells the electron spin within the orbital (

m

s ) There are two possible values: + 1/2 or – 1/2 They indicate the two opposite directions of electron spin – which produce oppositely directed magnetic fields.

Memorize

The “s” orbital

The “p” orbitals

The “d” orbitals

The “f” orbital

Atomic Orbitals: Putting Them Together http://www.kentchemistry.com/links/AtomicStructure/PauliHundsRule.htm

Be Able To:

1. Assign a set of four quantum number to each electron in an atom.

2. Recognize a valid set of quantum numbers 3. Describe atomic orbitals using quantum numbers.

4. Determine the # of orbitals and/or electrons in a given energy level or sublevel.

5. State the order of orbital energies from highest to lowest.

Writing Electron Configurations

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 5d 10 6p 6 7s 2 5f 14 6d 10 7p 6 6f 14 7d 10

6 7 2 3 4 5 Group Period Table 7-2: Electron Configuration and Energy Levels for the Periodic Table of the Elements 1 2 s-Orbitals 3 4 5 6 7 8 d-Orbitals 9 10 11 12 13 14 15 16 p-Orbitals 17 18 1

1s 1 1s 2 1s 1 1s 2 2s 1 3s 1 4s 1 5s 1 6s 1 7s 1 2s 2 3s 2 4s 2 5s 2 6s 2 7s 2

* **

3d 1 4d 1 5d 1 6d 1 3d 2 3d 3 4d 2 4d 3 5d 2 5d 3 6d 2 6d 3 3d 4 3d 5 3d 6 3d 7 4d 4 4d 5 4d 6 4d 7 5d 6d 4 4 5d 6d 5 5 5d 6d 6 6 5d 6d 7 7 3d 8 4d 8 5d 8 6d 8 2p 1 3p 1 3d 9 3d 10 4p 1 4d 9 4d 10 5p 1 5d 9 5d 10 6p 1 6d 9 6d 10 7p 1 2p 2 3p 2 4p 2 5p 2 6p 2 7p 2 2p 3 2p 4 2p 5 2p 6 3p 3 3p 4 3p 5 3p 6 4p 3 4p 4 4p 5 4p 6 5p 3 5p 4 5p 5 5p 6 6p 3 6p 4 6p 5 6p 6 7p 3 7p 4 7p 5 7p 6

* Lanthanoids ** Actinoids f-Orbitals

4f 1 5f 1 4f 2 5f 2 4f 3 5f 3 4f 4 5f 4 4f 5 5f 5 4f 6 5f 6 4f 7 5f 7 4f 8 5f 8 4f 9 5f 9 4f 10 4f 11 5f 10 5f 11 4f 12 4f 13 4f 14 5f 12 5f 13 5f 14

Orbital Notation

One way: Nitrogen Another way: Aluminum

Pauli Exclusion Principle

Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n,

l

,

m l

,

m

s ) NO! YES!

Hund’s Rule

Hund’s Rule – For degenerate orbitals, minimum energy is obtained when the number of electrons with the same spin is maximized.

Degenerate – means same sublevel