Quantum Theory and the
Electronic Structure of Atoms
Chapter 7
1
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
2
Properties of Waves
Wavelength (l) is the distance between identical points on
successive waves.
Amplitude is the vertical distance from the midline of a
wave to the peak or trough.
Frequency (n) is the number of waves that pass through a
particular point in 1 second (Hz = 1 cycle/s).
The speed (u) of the wave = l x n
3
Review of Concept
Which of the waves shown has (a) the highest
frequency (b) the longest wavelength (c) the
greatest amplitude?
4
Maxwell (1873), proposed that visible light consists of
electromagnetic waves.
Electromagnetic
radiation is the emission
and transmission of energy
in the form of
electromagnetic waves.
Speed of light (c) in vacuum = 3.00 x 108 m/s
All electromagnetic radiation
lxn=c
5
Example 7.1
Pg 279
The wavelength of the green light from a traffic signal is
centered at 522 nm. What is the frequency of this radiation?
7
Mystery #1, “Heated Solids Problem”
Solved by Planck in 1900
When solids are heated, they emit electromagnetic radiation
over a wide range of wavelengths.
Radiant energy emitted by an object at a certain temperature
depends on its wavelength.
Energy (light) is emitted or
absorbed in discrete units
(quantum).
E=hxn
Planck’s constant (h)
h = 6.63 x 10-34 J•s
E = hc / λ
Because  = c/λ
h = 6.63 x 10-34 J•s
8
Review of Concept
Why is radiation only in the UV but not the
visible or infrared region responsible for sun
tanning?
9
Example 7.2
Pg 282
Calculate the energy (in joules) of
(a) a photon with a wavelength of 5.00 × 104 nm
(infrared region)
(b) a photon with a wavelength of 5.00 × 10−2 nm (X ray
region)
Mystery #2, “Photoelectric Effect”
Solved by Einstein in 1905
hn
Light has both:
1. wave nature
2. particle nature
KE e-
Photoelectric effect phenomenon in
which electrons are ejected from the
surface of certain metals exposed to light
of at least a certain minimum frequency
(threshold frequency)
Photon is a “particle” of light
11
Bohr’s Theory of the Hydrogen
atom
12
Energize
the
sample
Line Emission Spectrum of Hydrogen Atoms
13
14
Bohr’s Model of
the Atom (1913)
1. e- can only have specific
(quantized) energy
values
2. light is emitted as emoves from one energy
level to a lower energy
level
En = −RH(
1
n2
)
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
15
E = hn
E = hn
16
Ephoton = DE = Ef - Ei
ni = 3
ni = 3
ni = 2
nf = 2
1
Ef = -RH ( 2
nf
1
Ei = -RH ( 2
ni
1
DE = RH( 2
ni
)
)
1
n2f
nnf f==11
17
)
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Example 7.4
Pg 288
What is the wavelength of a photon (in nanometers) emitted
during a transition from the ni = 5 state to the nf = 2 state in the
hydrogen atom?
THE DUEL NATURE OF THE
ELECTRON
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Standing Waves
21
Why is e- energy quantized?
De Broglie (1924) reasoned
that e- is both particle and
wave.
2pr = nl
h
l = mv
v = velocity of em = mass of e22
Example 7.5
Pg 292
QUANTUM MECHANICS
24
Heisenberg Uncertainty principle
Δx Δp ≥ h
4π
25
Schrodinger Wave Equation
In 1926 Schrodinger wrote an equation that
described both the particle and wave nature of the eWave function (y) describes:
1. energy of e- with a given y
2. probability of finding e- in a volume of space y2
Schrodinger’s equation can only be
solved exactly for the hydrogen atom.
Must approximate its solution for
multi-electron systems.
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QUANTUM NUMBERS
27
principal quantum number n
n = 1, 2, 3, 4, ….
distance of e- from the nucleus
n=1
n=2
n=3
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Sublevels
Shape of the “volume” of space that the e- occupies
Sublevels:
s orbital
p orbital
d orbital
f orbital
29
s orbital (1 orientation: sphere)
p orbital (3 orientations: dumbbells)
d orbital (5 orientations:
double dumbbells)
f orbital (7 orientations)
Spin
34
Energy of orbitals in a single electron atom
Energy only depends on principal quantum number n
n=3
n=2
En = -RH (
1
n2
)
n=1
35
Energy of orbitals in a multi-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 0
n=2 l = 0
n=3 l = 1
n=2 l = 1
n=1 l = 0
36
Electron configuration is how the electrons are
distributed among the various atomic orbitals in an
atom.
number of electrons
in the orbital
1s1
principal quantum
number n
Sublevel (shape)
Orbital diagram
H
1s1
37
“Fill up” electrons in lowest energy orbitals (Aufbau principle)
38
Pauli exclusion principle - no two electrons in an atom
can have the same four quantum numbers.
Each seat is uniquely identified (E, R12, S8).
Each seat can hold only one individual at a
time.
39
Paramagnetic
unpaired electrons
2p
Diamagnetic
all electrons paired
2p
40
Shielding Effect
• Why is the 2s orbital lower in
energy than the 2p?
• “shielding” reduces the
electrostatic attraction
• Energy difference also
depends on orbital shape
41
The most stable arrangement of electrons in
subshells is the one with the greatest number of
parallel spins (Hund’s rule).
42
Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
43
Outermost subshell being filled with electrons
44
Example 7.11
Pg 309
An oxygen atom has a total of eight electrons. Write the ground
state electron configuration and orbital diagram.
46
Noble Gas Configuration
Ex: Aluminum
e− configuration: 1s22s22p63s23p1
preceding noble gas is Ne: 1s22s22p6
noble gas configuration: [Ne] 3s23p1
47
Example
Write the noble gas configuration and the noble gas orbital
diagram for sulfur (S).