Quantum Theory and the Electronic
Structure of Atoms
Chapter 7
Our world until the end of the nineteenth century
The Macroscopic World
classical theory of
electromagnetic Radiation
by Maxwell
Matter
Radiation (Light)
Newtonian Mechanics
(Newton’s laws),
Thermodynamics
Studied and characterized by Classical Physics
The Microscopic World
For chemists it is the world of atoms and molecules
The end of the nineteenth century witnessed the birth of the
quantum theory and the discovery of the microscopic world
Studied and characterized by quantum physics
In order to understand the quantum theory and the microscopic
world, we need to Understand classical properties of matter
and waves
Waves
•
The distance between corresponding points
on adjacent waves is the
wavelength
(
⤮
•
The number of waves
passing a given point per
unit of time is the
frequency (
)
.
•
For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
Electromagnetic Radiation
•
All electromagnetic radiation travels at the same velocity
•
the speed of light (
c
), 3.0
10
8
m/s.
•
Therefore,
c
=
The Nature of Energy of Radiation
•
The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
•
Max Planck
explained it
by assuming that
energy comes in
packets called
quanta
.
•
Einstein used this
assumption to explain the
photoelectric effect.
•
He concluded that energy
is proportional to
frequency:
E
=
h
where
h
is Planck’s
constant, 6.63
10
−
34
J

s.
The Nature of Energy of Radiation
The Nature of Energy of Radiation
c
c
h
E
•
Therefore, if one knows the
Wavelength or the frequency of
light, one can calculate the energy
in one photon, or packet,
of that light:
photon
photon
h
E
or
where
Pay attention to units
Another mystery involved the emission spectra
observed from energy emitted by atoms and
molecules.
VIS
40 %
IR
51 %
UV
9 %
nm
500
1000
nm
500
max
Solar radiation intensity
The Nature of Energy of Radiation
Atomic spectra: http://astro.u

strasbg.fr/~koppen/discharge/index.html
Demo: H, He, and Ne atoms
Only a
line spectrum
of
discrete wavelengths is
observed.
Emission Spectrum of the Hydrogen Atom
Quantization of Energy of Electrons
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this way:
1. Electrons in an atom can
only occupy certain orbits
(corresponding to certain
energies).
1.
Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
2.
Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
Bohr Model for the energy Levels of the hydrogen atom
2
H
n
n
R
E
1

18
H
cm
737
,
109
J
10
18
.
2
R
,....
3
,
2
,
1
n
n
1
2
3
4
5
n
H
R
4
R
H
9
R
H
16
R
H
0
absorption
emission
2
i
2
f
H
2
i
H
2
f
H
n
1
n
1
R
n
R
n
R
E
2
i
2
f
H
n
1
n
1
R
h
h
E
E
E
i
f
2
H
n
n
R
E
1
H
cm
737
,
109
R
,....
3
,
2
,
1
n
Frequencies of Absorption and Emission Transitions
In The hydrogen atom
Absorption
Emission
f
E
f
E
i
E
i
E
h
E
E
E
i
f
h
E
E
E
i
f
de Broglie’s Postulate (Wave

Particle Duality of Matter)
p
h
m
v
mv
P
Particle property
Wave property
De Broglie argued that both light and matter obey his equation
Why the wave property of matter is important for microscopic
objects while it is not important for macroscopic objects?
a. What is the value of
of an electron traveling at 1.00% of the speed
of light?
b. What is the value of
of a person (m = 62.6 kg) moving at 1m/s?
Let us carry out the following exercises
mv
P
;
p
h
Answer
This wavelength is about five times greater than the radius of the H atom
A
43
.
2
10
3
)
kg
(
10
1
.
9
s
.
J
10
626
.
6
6
31
34
a.
A
10
06
.
1
25
This wavelength is too small to be detected
b.
a. Electron diffraction (Al)
b. X

ray diffraction experiment (Al)
http://www.matter.org.uk/diffraction/introduction/what_is_diffraction.htm
de Broglie Waves Are Observed Experimentally
http://jchemed.chem.wisc.edu/JCEWWW/Articles/WavePacket/WavePacket.html
2
h
;
2
P
.
x
The Heisenberg Uncertainty Principle
2
)
mv
(
.
x
or
In many cases, our uncertainty of the whereabouts
of an electron is greater than the size of the atom
itself!
Quantum Mechanics
•
Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle nature
of matter could be
incorporated.
•
It is known as
quantum
mechanics
.
Quantum Mechanics
•
The wave equation is
designated with a lower
case Greek
psi
(
).
•
The square of the wave
equation,
2
, gives a
probability density map of
where an electron has a
certain statistical likelihood
of being at any given instant
in time.
Quantum Numbers
•
Solving the wave equation gives a set of wave
functions, or
orbitals
, and their corresponding
energies.
•
Each orbital describes a spatial distribution of
electron density.
•
An orbital is described by a set of three
quantum
numbers
.
Principal Quantum Number,
n
•
The principal quantum number,
n
, describes the
energy level on which the orbital resides.
•
The values of
n
are integers ≥ 0.
Azimuthal Quantum Number,
l
•
This quantum number defines the shape of
the orbital.
•
Allowed values of
l
are integers ranging from
0 to
n
−
1.
•
We use letter designations to communicate
the different values of
l
and, therefore, the
shapes and types of orbitals.
Azimuthal Quantum Number,
l
Value of
l
0
1
2
3
Type of orbital
s
p
d
f
Magnetic Quantum Number,
m
l
•
Describes the three

dimensional orientation
of the orbital.
•
Values are integers ranging from

l
to
l
:
−
l
≤
m
l
≤
l.
•
Therefore, on any given energy level, there
can be up to 1
s
orbital, 3
p
orbitals, 5
d
orbitals, 7
f
orbitals, etc.
Magnetic Quantum Number,
m
l
•
Orbitals with the same value of
n
form a
shell
.
•
Different orbital types within a shell are
subshells
.
s
Orbitals
Spherical in shape.
Radius of sphere increases
with increasing value of
n.
l
= 0
m
l
= 0
s
Orbitals
Observing a graph of
probabilities of finding
an electron versus
distance from the
nucleus, we see that
s
orbitals possess
n
−
1
nodes
, or regions
where there is 0
probability of finding an
electron.
p
Orbitals
Have two lobes with a node between them.
l
= 1
m
l
= +1, 0,

1
d
Orbitals
Four of the five orbitals
have 4 lobes;
the other resembles a
p
orbital with a doughnut
around the center.
l
= 2
m
l
= +2, +1, 0,

1,

2
Energies of Orbitals
•
For a one

electron
hydrogen atom,
orbitals on the same
energy level have the
same energy.
•
That is, they are
degenerate
.
Energies of Orbitals
•
As the number of
electrons increases,
though, so does the
repulsion between
them.
•
Therefore, in many

electron atoms,
orbitals on the same
energy level are no
longer degenerate.
Spin Quantum Number,
m
s
•
In the 1920s, it was
discovered that two
electrons in the same
orbital do not have
exactly the same energy.
•
The “spin” of an electron
describes its magnetic
field, which affects its
energy.
Spin Quantum Number,
m
s
•
This led to a fourth
quantum number, the
spin quantum number,
m
s
.
•
The spin quantum
number has only 2
allowed values: +1/2
and
−
1/2.
Pauli Exclusion Principle
•
No two electrons in the
same atom can have
exactly the same energy.
•
For example, no two
electrons in the same
atom can have identical
sets of quantum
numbers.
Electron Configurations
Distribution of all electrons in an atom consist of
5
p
4
4

Number denoting the energy level
p

Letter denoting the type of orbital
5

Superscript denoting the number of electrons in those
orbitals
Orbital Diagrams
•
Each box represents one
orbital.
•
Half

arrows represent
the electrons.
•
The direction of the
arrow represents the
spin of the electron.
Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained
when the number of
electrons with the
same spin is
maximized.”
Periodic Table
•
We fill orbitals in
increasing order of
energy.
•
Different blocks on
the periodic table,
then correspond to
different types of
orbitals.
Some Anomalies
Some irregularities occur when there are enough
electrons to half

fill
s
and
d
orbitals on a given row.
For instance, the electron
configuration for copper is
[Ar] 4
s
1
3
d
5
rather than the expected
[Ar] 4
s
2
3
d
4
.
These anomalies occur
in
f

block atoms, as well.
This occurs because the 4
s
and 3
d
orbitals are very
close in energy.
8
O
11
Na
19
K
Detailed and Abbreviated Electron Configurations
Of Metals and Nonmetals
16
S
Detailed and Abbreviated Electron Configurations
Of Transition Metals
21
Sc
24
Cr
25
Mn
29
Cu
Diamagnetism and Paramagnetism
Paramagnetic substances
Any substance that possesses
net nonzero
electron spin
quantum number and therefore attracted by a magnet
6
2
18
26
d
3
[Ar]4s
:
Fe
1
2
10
13
p
3
[Ne]3s
:
Al
Diamagnetic substances
Any substance that possesses
net zero
electron spin
and therefore not attracted by a magnet
10
2
36
48
d
4
5s
:
[Kr]
:
Cd
10
2
18
30
d
3
[Ar]4s
:
Zn
A Very Useful Tool For Understanding Electron
Configuration of Atoms
Electron Configuration, From Prentice Hall
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