CHAPTER 6:CHAPTER 6:

ELECTRONIC STRUCTUREELECTRONIC STRUCTURE

The Nature of Light

Quantized Energy/Photons

– Photoelectric Effect

Bohr’s Model of Hydrogen

Wave Behavior of Matter

– Uncertainty Principle

Quantum Mechanics/Atomic Orbitals

– Quantum Numbers/Orbitals

Representations of Orbitals

Many-Electron Atoms– Effective Nuclear Charge– Relative Energies of Orbitals– Electron Spin/Pauli Excl. Principle

Electron Configurations

Periodic Relationships

Wave Nature of Light

Electromagnetic Radiation– electric & magnetic components with

periodic oscillations

– length in m, cm, mm, m, nm,

– frequency in cycles/sec or hertz, – = c where c = speed of light

long wavelength

short wavelength

Quantized Energy and Photons Black Body Radiation

– heated bodies radiate light and depends on temperature

– Planck -- energy released in ‘packets’– smallest ‘packet’ is a quantum– energy of one quantum , E =

• , Planck’s constant = 6.63 x 10 - 34 J-s

Practice Ex. 6.2: A laser that emits light in short pulses has a

= 4.69 x 1014 s-1 and deposits 1.3 x 10 -2 J of

energy during each pulse. How many quanta of energy does each pulse deposit?• E = • E of 1 quantum = (6.63 x 10 -34 J-s) (4.69 x 1014 s-1) =

3.11 x 10 -19 J/quanta

• 1.3 x 10 -2 J = 4.2 x 10 16 quanta 3.11 x 10 -19 J/quanta

Photoelectric Effect– metals exposed to light, radiant energy, emit

electrons– each metal has a minimum of light– Einstein’s ‘photons’ of light must have sufficient

threshold energy – energy of photon depends on the of light, E =

• high frequency, short wavelength ( = c/) high energy

– light is also quantized, 1 photon = 1 quanta

metal surface

photon with E > threshold

e - with kinetic energy = photon E - threshold E e -

Bohr’s Model of the Hydrogen Atom

Line Spectra– spectrum -- light composed of different

wavelengths and energies

– contiunous spectrum -- continuous range of ’s and E’s

– line spectrum -- non-continuous spectrum (only specific ’s and E’s)

– Balmer 1800’s = C (1/22 - 1/n2) n = 3, 4, 5, 6 C = 3.29 x 10 15 s - 1

400 450 500 550 600

Hydrogen Line Spectrum

Bohr’s Model

– electrons in “orbits” around nucleus– “orbits” are allowed energies which are

quantized– to move between quantized orbits,

electrons must either absorb or emit quanta of energy

– E = - RH ( 1/n2 ) n = 1, 2, 3, 4 . . . . . principle quantum number

– RH (Rydberg constant) = 2.18 x 10 -18 J

e-

e-

nucleusnucleus

n=1 n=2 n=3 n=4

e-

Energyabsorption

nucleusnucleus

e-

e-

n=1 n=2 n=3 n=4

Energyemission

e-

e-

nucleus

n=1 n=2 n=3 n=4

E1

E2 E3

E = Ef - Ei = E1 > E2 > E3

– energy of the transition depends on the levels

E = Ef - Ei = or E = = Ef - Ei

• = (RH/ )(1/ni2 - 1/nf

2)

or E = RH (1/ni2 - 1/nf

2)

• ni = initial level of electron

• nf = final level of electron

E or is +radiant energy absorbed

nucleus

n=1 n=2 n=3 n=4

E or is -radiant energy emitted

n=1 2 3 4 5 6

Balmer Series - visible H line spectrum

H

Lyman Series - in the uv

Wave Behavior of Matter

Basis for Quantum Mechanics– De Broglie wave equation

• = “matter” waves mv

– Uncertainty Principle -- Werner Heisenberg• fundamental limitation on how precisely

we can know the location and momentum

Quantum Mechanics and Atomic Orbitals

Quantum Mechanics or Wave Mechanics– mathematical method of predicting the

behavior of electrons

– wave functions are solutions to these mathematical equations

– wave functions predict the “probability” of finding electron density, 2

– wavefunction describes “orbitals”

Orbitals & Quantum Numbers

– orbitals describe volumes of electron density

– orbitals are of different types s, p, d, f

– each orbital is described by a set of quantum

numbers n, , m

• each quantum number has an allowed set of values

Quantum Numbers

n can have values of 1, 2, 3, 4, 5 . . . . – describes the major shell or distance from the nucleus

can have values of 0, 1, 2, 3 . . . n-1– describes the type of subshell

• = 0 s subshell = 1 p subshell

• = 2 d subshell = 3 f subshell

m can have values of - . . . 0 . . . + – describes which orbital within the subshell

n=1 n=2

nucleus+

s

s

pp

p

sp

pp

dd

ddd

s p p p

dd

dd

d

fffffff

n=4n=3

s

p

d

f

= 0

= 1

= 2

= 3

– total number of orbitals in a subshell is n2

– maximum number of electrons in a subshell is 2n2

– maximum number of electrons in an orbital is 2

s last quantum number describes the

spin on an

electron– each electron has a spin +½ or -½

n=1 n=2

nucleus+

s

s

pp

p

sp

pp

dd

ddd

s p p p

dd

dd

d

fffffff

n=4n=3

s

p

d

f

= 0

= 1

= 2

= 3-1

0

+1

-2-1

0

+1+2

-2-3

-10+1+2+3

0m

m

mm

Orbital Pictures

s-type orbitals

– always one orbital in the subshell with = 0

and m = 0– are spherical– differences between s orbitals in different major

shells (with different n values)• size

– remember, we’re talking in terms of probability of the occurrence of electron density

Notice that we are looking at a volume of diffuse electronelectron density as pictured by the many small dots

s orbital cross-sections

p-type orbitals

– always three orbitals in the subshell with

= 1 and m = -1, 0, +1

– are dumb-bell shaped

– different m values are oriented along

different axes, x, y, or z (px, py, pz)

– differences between p orbitals in different

major shells

• size

d-type orbitals

– always five orbitals in the subshell with =

2 and m = -2, -1, 0 +1, +2

– most are four-lobed

– different m values are oriented differently

on x, y, z axes dz2, dx2-y2, dxy, dxz, dyz

– differences between d orbitals in different

major shells

• size

Energ

y

s

s p p p

s d d d d d

d d d d d f f f f f f f

p p p

Orbital/Subshell energy levels in the hydrogen atom

n=1

s p p pn=2

n=3

n=4

Multi-electron Atoms screening effect

– inner electrons “shield” the nuclear charge from outer electrons

– energy levels of subshells within major shells become different

– nuclear charge experience by outer electrons is decreased

• Zeff = Z - S

• Zeff decreases with increasing value

Energ

y

s

Orbital/Subshell energy levels in multi electron atoms

n=1

s

p p p

n=2

sn=3

n=2

p p pn=3

d d d d dn=3

Pauli Exclusion Principle– no two electrons can have the same exact set of quantum

numbers• consider this orbital and its two electrons

• quantum numbers are n = 2, = 1, m = 0

• the two electrons must have a quantum number that is different -- s = +½ and - ½

– First electron has spin +½ and second electron -½

p p pn=2

= 1 m = -1 0 +1

Electron Configurations There is a pattern in the energy levels

that hold electrons– electrons fill up the pattern from the lowest

energy to the highest energy level– 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p

7s

– for 1H for 2He 1s 1s

– 3Li 4Be 1s 2s 1s 2s

Hund’s Rule– electrons enter degenerate orbitals in a subshell one at a time

until the subshell is half-filled

– 5B 6C 1s 2s 2p 1s 2s 2p

– 7N 1s 2s 2p

– 8O 1s 2s 2p

Periods 1, 2 & 3– 3Li

1s 2s

– 11Na 1s 2s 2p 3s

– 19K 1s 2s 2p 3s 3p 4s

– outer shell is called the valence shell

Group 1– 3Li

1s 2s

– 11Na 1s 2s 2p 3s

– 19K 1s 2s 2p 3s 3p 4s

[Ne][Ne] 3s1

[Ar][Ar] 4s1

– all group I elements have electron configuration• [nobel gas] ns1

– all group II elements have electron configuration• [nobel gas] ns2

– all group III elements have electron configuration

• [nobel gas] ns2 np1

– group IV elements• [nobel gas] ns2 np2

– group V elements• [novel gas] ns2 np3 etc.

1 2 3 4 5 6 7 8

s1 s2 p3 p4 p5 p6 p7 p8

1

2

3

4

5

6

7

d1 . . . . . . . . . . . . . . d10

Electron Configuration & Periodic Table

ns1

ns2 ns2p1 ns2p2 ns2p3 ns2p4 ns2p5

ns2p6

ns2 (n-1)d1-10