Review Chapter 8:
The Quantum
Mechanical Atom
Chemistry: The Molecular Nature of Matter,
6th edition
By Jesperson, Brady, & Hyslop
Chapter 8 Concepts
 Connect (& calculate) wavelength, frequency, and the energy of the
wave.
 Calculate the energy emitted or absorbed by an electron moving to or
from an excited state
 Understand & communicate the duel wave-partial duality of light and
electrons
 Understand & communicate the collapsing atom paradox
 Understand & communicate quantized energy of an electron
 Electron book-keeping: quantum numbers, e- configurations, & orbital
diagrams
 The Heisenberg Uncertainty Principle & electron density (probability)
 The shape of orbitals
 Calculate Zeff
 Periodic trends dependent on Zeff
2
Memorize
 =c
c = speed of light = 2.9979 × 108 m/s
E=h
h = Planck’s constant = 6.626 × 10–34 J s
E = NAh
NA = 6.02 × 1023 atoms/mole
 1
1
1 

 RH

2
2


n
n
2 
 1
RH = 109,678 cm–1 = Rydberg constant
Zeff = # protons - # core electrons
Electromagnetic Radiation
low energy, long waves
high energy, short waves
Quantum Mechanics
• Light behaves as a particle & a wave
• Photon is a particle of light
• Energy is Quantized:
• Photoelectric effect
• excited electron emit only specific frequencies of light (Energy)
• Electrons also behave as a particle & a wave
• Double slit experiment: electrons behave as a wave! And a particle!
• Collapsing wave paradox
n 2h 2
• If E quantized an electron cannot have E = 0 E =
2
•
•
•
•
Neat Videos:
https://www.youtube.com/watch?v=Xmq_FJd1o
UQ (wave-particle, short)
https://www.youtube.com/watch?v=a8FTr2qMut
A (heisenburg uncertainty principle, short)
https://www.youtube.com/watch?v=7vcUvp3vwg (heisenburg uncertainty principle,
short)
https://www.youtube.com/watch?v=QVPIGtGcY
E0 (great NOVA episode ~ 1 hr)
http://abyss.uoregon.edu/~js/glossary/wave_particle.html
8mL
Quantum Numbers
n = principal quantum number = 1, 2, 3, 4, …, n
 Determine n by the row the element is in
ℓ = secondary quantum number = 0, 1, 2, …, n-1
 Determine by the section of the periodic table: group 1A &
2A = s = 0, group 3A - 8A = p = 1, transition metals = d = 2,
lanthanide & actinides = f = 3.
mℓ = magnetic quantum number = + ℓ, ..., 0, ..., - ℓ
 Determined by column element is in. Left to right positive to
negative, but remember each orbital has two electrons:
Ex: p orbitals:
= __ __ __
+1 0 -1 +1 0 -1
+1 0 -1
ms = magnetic spin quantum number = + ½ , - ½
 First electron placed = + ½ and the second = - ½
e- Configurations & Orbital Diagrams
Electron Configurations will follow the order:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 ….
6s
5p
4d
5s
4p
3d
4s
Energy
3p
3s
2p
2s
1s
Abbreviate:
[Nobel gas]
in n-1 row
Aufbau Principle: Fill electrons in
the orbital diagram in order of
increasing energy:
s, (n-2)f, (n-1)d, p
Pauli Exclusion Principle: 2
__
electrons per orbital with opposite
spins
Hund’s Rule: Fill all orbitals of the
same energy with one electron
before pairing electrons.
__ __ __
Orbital Shapes
Orbitals
& corresponding m
dx2-y2
s
px
pz
py
dxz
dz2
dyz
s: spherical nodes = n-1
0 planar nodes
p: spherical nodes = n-1
1 planar node
d: spherical nodes = n-1
2 planar nodes
f: spherical nodes = n-1
3 planar nodes
dxy
Periodic Trends
Electron Affinity
INCREASING
Ionization Energy
INCREASING
Atom Size
INCREASING
Atom Size: Zeff the same down a column, but distance from valence e- to nucleus increases,
therefore size increases. Zeff increases across a row therefore size decreases.
Ionization Energy (IE): The energy required to remove an electron from the valence shell
increases with Zeff and decreases with increased distance between the nucleus and electron.
Electron Affinity (EA): This is the opposite of ionization energy, it is how easy it is to add an
electron to an atom, and follows the same trend as IE energy.
Problem Set 8 A
1. Which electromagnetic radiation has a higher energy? Radio waves or
microwaves? UV light or X rays?
2. How does thermal imaging work? (Use what you have learned about the
electromagnetic spectrum to briefly explain).
3. Blue, red, and green lasers have wavelengths of 445 nm, 635 nm, and 532
nm respectively what are their frequencies, and what is the energy in Joules
of a photon from each laser?
4. In Neon there is a line with the frequency of 4.546 x1014 Hz. What is its
wavelength and color of the line? And what is the energy of each of its
photons?
5. What is the wavelength of light (in nm) that is emitted when an excited
electron in the hydrogen atom falls from n = 5 to n = 3? Would you expect to
be able to see the light emitted?
6. How many grams of water could have its temperature raised by 7.000°C by a
mole of photons that have a wavelength of 450.0 nm?
(sH2O @ 0C = 4.179 J/gC)
Problem Set 8 B
7. Would you expect the waves above to increase or decrease in amplitude
when added together?
8. With the strong attractive force between the positively charged nucleus
and an electron, why doesn’t the nucleus capture electrons?
9. Determine quantum numbers for Boron. It’s electron configuration is 1(s)2
2(s)2 2(p)1
10. What is the electron configuration for Nitrogen? N-3?
11. Is Selenium (Se) paramagnetic or diamagnetic?
12. Draw an orbital diagram for Indium (In).
Problem Set 8 C
13. What is the abbreviated electron configuration and abbreviated orbital diagram for
the following elements:
a) Fe
b) At
c) Ra
d) Sb
14. What is the valence electron configuration for O and Se?
15. Which atom has the smallest radius? Ca, Na, Mg, Ar, K?
16. Which atom has the smallest ionization energy? C, Cs, K, Mg, Ba?
17. Which atom has the greatest electron affinity? O, I, Ne, Ar, Cl, K, Ga?
Problem Set 8 Solutions
1. Microwaves. X-rays.
2. Thermal imaging detects infrared radiation, which is heat. Higher
temperature bodies emit more infrared radiation.
3. Blue: 6.74 x1014 s-1; 4.74 x10-19 J Red: 4.72 x1014 s-1; 3.13 x10-19 J Green:
5.64 x1014 s-1; 3.74 x10-19 J
4. Wavelength = 660 Color = Red Energy = 1.467 x 1016 J
5. Wavelength = 1282 nm (1.282 x10-6 m) Not in visible range
6. Mass of water = 9093 g
7. Decrease amplitude
1. Lowest quantum number n = 1, and Energy of an electron is inversely
proportional to n, therefore it can never have an energy of 0 because n
cannot equal 0.
2. n = 2 l = 1 ml = 1 ms = + ½
1. 1(s)2 2(s)2 2(p)3. 1(s)2 2(s)2 2(p)6
1. Paramagnetic (2 unpaired electrons)
Problem Set 8 Solutions
6s
12. .
5p
4d
5s
4p
3d
4s
Energy
3p
3s
2p
2s
1s
13. Answers:
a) [Ar] 4s2 3d6
[Ar] 3d __ __ __ __ __ 4s __
b) [Xe] 6s2 4f14 5d10 6p5
c) [Xe] 4f __ __ __ __ __ __ __ 5d __ __ __ __ __ 6s __ 6p __ __ __
d) [Rn] 7s2 [Rn] 7s __
e) [Kr] 5s2 4d10 5p3
[Kr] 4d __ __ __ __ __ 5s __ 5p __ __ __
14. O: 2s2 2p4
15. Ar
Se: 4s2 4p4
16. Cs
17. Cl