CHAPTER 6:
ELECTRONIC 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, mm, nm, l
– frequency in cycles/sec or hertz, n
– nl = c where c = speed of light
l
l
long wavelength
short wavelength
Quantized Energy and Photons
Black Body Radiation
– heated bodies radiate light and l depends
on temperature
– Planck -- energy released in ‘packets’
– smallest ‘packet’ is a quantum
– energy of one quantum , E = hn
• h, Planck’s constant = 6.63 x 10 - 34 J-s
Practice Ex. 6.2:
A laser that emits light in short pulses has a
n = 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 = hn
• 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
3.11 x 10 -19 J/quanta
= 4.2 x 10
16
quanta
Photoelectric Effect
– metals exposed to light, radiant energy, emit
electrons
– each metal has a minimum n of light
– Einstein’s ‘photons’ of light must have sufficient
threshold energy
– energy of photon depends on the n of light, E = hn
• high frequency, short wavelength (l = c/n)  high
energy
– light is also quantized, 1 photon = 1 quanta
photon with
E > threshold
e - with kinetic energy =
photon E - threshold E
e-
metal surface
Bohr’s Model of the Hydrogen Atom
Line Spectra
– spectrum -- light composed of different wavelengths
and energies
– contiunous spectrum -- continuous range of l’s and E’s
– line spectrum -- non-continuous spectrum (only specific
l’s and E’s)
– Balmer 1800’s
n = 3, 4, 5, 6
n = C (1/22 - 1/n2)
C = 3.29 x 10 15 s - 1
Hydrogen Line Spectrum
400
450
500
550
600
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-
e-
Energy
absorption
nucleus
n=1
n=2
n=3
n=4
eEnergy
emission
enucleus
n=1
n=2
n=3
n=4
DE = Ef - Ei = hn
DE1 > DE2 > DE3
DE3
DE2
DE1
e-
enucleus
n=1
n=2
n=3
n=4
– energy of the transition depends on the levels
DE = Ef - Ei = hn or
•
DE = n = Ef - Ei
h
n = (RH/ h )(1/ni2 - 1/nf2)
or
DE = RH (1/ni2 - 1/nf2)
• ni = initial level of electron
• nf = final level of electron
DE or n is +
radiant energy absorbed
DE or n is radiant energy
emitted
nucleus
n=1
n=2
n=3
n=4
Balmer Series - visible
H line spectrum
Lyman Series
- in the uv
H
n=1
2
3
4 56
Wave Behavior of Matter
Basis for Quantum Mechanics
– De Broglie wave equation
• l= h
mv
“matter” waves
– 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, Y2
– 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, l, 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
l  can have values of 0, 1, 2, 3 . . . n-1
– describes the type of subshell
• l=0
• l=2
s subshell
d subshell
l=1
l=3
p subshell
f subshell
m  can have values of - l . . . 0 . . . + l
– describes which orbital within the subshell
s
pp
p
s l = 0
s
p
d
p
d
p l = 1
d
p
d
d
s
f
d
p
p
s
n=1
f
d
p
nucleus
+
d l = 2
n=2
d
d
d
n=3
f
f
f
f
f
f
n=4
l = 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
s
pp
p
s l = 0
s
p
d
p
d
p
d
d
d l = 2
m d
-2
m
m
f l = 3
d -1
f -3
p -1
d
0 f -2
0
p
d
-1
p +1
d +1 f
0
d +2 f
f +1
f +2
f +3
s
m
s 0
nucleus
+
p l = 1
n=1
n=2
n=3
n=4
Orbital Pictures
s-type orbitals
– always one orbital in the subshell with l = 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 electron
electron density as pictured by the many small dots
s orbital
crosssections
p-type orbitals
– always three orbitals in the subshell with l = 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 l = 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
Energy
n=4
s
p p p
d d d d d
n=3
s
p p p
d d d d d
n=2
s
p p p
n=1
s
f f f f f f f
Orbital/Subshell
energy levels in
the hydrogen atom
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
l value
Energy
n=3
d d d d d
n=3
n=3
p p p
s
n=2
p p p
n=2
s
n=1
s
Orbital/Subshell
energy levels in
multi electron
atoms
Pauli Exclusion Principle
– no two electrons can have the same exact set of
quantum numbers
• consider this orbital and its two electrons
n=2
p p p
l = 1 m = -1 0 +1
• quantum numbers are n = 2, l = 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
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
– 3Li
1s

1s
for 2He
2s
4Be

1s
 
1s
2s
Hund’s Rule
– electrons enter degenerate orbitals in a subshell
one at a time until the subshell is half-filled
– 5B
 
1s
2s
2p
6C
– 7N
 
1s 2s
2p
– 8O
 

1s 2s
2p


1s
2s
2p
Periods 1, 2 & 3
– 3Li 
1s
2s
– 11Na  
  
1s 2s
2p
– 19K  
  

1s 2s
2p
3s
  
3s
– outer shell is called the valence shell
3p
4s
Group 1
– 3Li 
1s
2s
– 11Na  
  
1s 2s
2p
3s
[Ne] 3s1
[Ne]
– 19K  
  

1s 2s
2p
[Ar]
  
3s
3p
[Ar] 4s1
4s
– 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
ns1
1
2
3
s2
ns p
ns2p1 ns2p2 ns2p3 ns2p4 ns2p5
ns2
s1
5 6 7 82 6
ns2 (n-1)d1-10
d1 . . . . . .
. . . . . . . . d10
p3 p4 p5 p6 p7 p8
4
5
6
7
Electron Configuration & Periodic Table