1
CHE 106: General Chemistry
CHAPTER
SIX
Copyright © James T. Spencer 1995 - 1999
Tyna L. Heise 2001-2002
All Rights Reserved
Prof. J. T. Spencer
CHE
106
Chapter Six: Electronic
Structure


2
Closer look at atomic inner workings
Prior to 1926, Many experiments in the structure
of matter showed several important relationships:
– Light has BOTH wavelike and particulate (solid
particle-like) properties.
– Even solid particles display BOTH wavelike and
particulate properties.
– Whether the wavelike or particulate properties
are predominantly observed depends upon the
nature of the experiment (what is being
measured).
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation

3
 = c
– where  = wavelength,  = frequency,
wavelength ()
c = light speed
amplitude
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
4
 = c
– where  = wavelength,  = frequency,
c = light speed
Gamma
UV/Vis Infrared Microwave Radio
X-ray
Wavelength (m)

10-11m
Prof. J. T. Spencer
10 m
CHE
106
Electromagnetic Radiation


5
Electromagnetic radiation consists of BOTH
electric and magnetic components. The wave
properties seen in radiation is due to the
oscillation of these properties
All radiation moves at the speed of light, so
wavelength and frequency are related
  = c
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
6
Sample exercise: A laser is used in eye
surgery to fuse detached retinas
produces radiation with a frequency
of 4.69 x 1014 s-1. What is the
wavelength of this radiation?
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
7
Sample exercise: A laser is used in eye
surgery to fuse detached retinas
produces radiation with a frequency
of 4.69 x 1014 s-1. What is the
wavelength of this radiation?
 = c
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
8
Sample exercise: A laser is used in eye
surgery to fuse detached retinas
produces radiation with a frequency
of 4.69 x 1014 s-1. What is the
wavelength of this radiation?
 = c
x(4.69 x 1014 s-1) = 3.00 x 108 m/s
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
9
Sample exercise: A laser is used in eye
surgery to fuse detached retinas
produces radiation with a frequency
of 4.69 x 1014 s-1. What is the
wavelength of this radiation?
 = c
x = 3.00 x 108 m/s
4.69 x 1014 s-1
Prof. J. T. Spencer
CHE
106
Electromagnetic Radiation
10
Sample exercise: A laser is used in eye
surgery to fuse detached retinas
produces radiation with a frequency
of 4.69 x 1014 s-1. What is the
wavelength of this radiation?
 = c
x = 3.00 x 108 m/s = 6.40 x 10-7 m
4.69 x 1014 s-1
Prof. J. T. Spencer
CHE
106
Visible Light

11
The rhodopsin molecule is the first link in the
chain that leads from light’s hitting the eye to the
brain’s acknowledging that light.
Rhodopsin
Prof. J. T. Spencer
CHE
106
Louis de Broglie
12
Light Had Both
Particulate and Wavelike Properties
HOW?
Duality of Nature
Relationships
(1892-1987)
Prof. J. T. Spencer
CHE
106
Light: Dual Properties

13
Light has both wave-like and particle-like nature
Particulate
Behavior
Wave-like
Behavior
electrons
ejected
from
bulk
material
Photoelectric Effect
Prof. J. T. Spencer
White
Light
Source
Dispersion by Prism
CHE
106
Matter: Dual Properties

14
Matter has both wave-like and particle-like nature
Particulate
Behavior
Wave-like
Behavior
electrons
ejected
Electron Ionization
Prof. J. T. Spencer
Electron
Beam
Source
Electron Diffraction
CHE
106
Max Planck

15
Blackbody radiation
2000°
I
1500°
•Wavelength distribution
of hot objects depends
upon temperature. (red
cooler than white)
predicted •Predictions on all
theory led to very poor
agreement
•Planck ASSUMED that
energy can be released
only in discrete packets

Prof. J. T. Spencer
CHE
106
Max Planck

16
Blackbody radiation
2000°
I
1500°

Prof. J. T. Spencer
•Assumed that energy
can be released only in
discrete ‘chunks’ of some
minimum size
predicted •gives the name ‘quanta’
to this minimum energy
absorbed or emitted
•proposes that this
energy is related to the
frequency of the
radiation
•Proposed E = hv
CHE
106
Microscopic Properties



17
Light energy may behave as waves or as small
particles (photons).
Particles may also behave as waves or as small
particles.
Both matter and energy (light) occur only in
discrete units (quantized).
Quantized
(can stand only on steps)
Prof. J. T. Spencer
Non-Quantized
(can stand at any position on the ramp)
CHE
106
What is Quantization

18
Examples of quantization (when only discrete
and defined quantities or states are possible):
Quantized
Non-Quantized
Piano
Stair Steps
Typewriter
Dollar Bills
Football Game Score
Light Switch (On/Off)
Energy
Matter
Violin or Guitar
Ramp
Pencil and Paper
Exchange rates
Long Jump Distance
Dimmer Switch
Prof. J. T. Spencer
CHE
106
What is Quantization
19
Sample exercise: A laser emits light
with a frequency of 4.69 x 1014 s-1.
What is the energy of one quantum of
this energy?
Prof. J. T. Spencer
CHE
106
What is Quantization
20
Sample exercise: A laser emits light
with a frequency of 4.69 x 1014 s-1.
What is the energy of one quantum of
this energy?
E = hv
Prof. J. T. Spencer
CHE
106
What is Quantization
21
Sample exercise: A laser emits light
with a frequency of 4.69 x 1014 s-1.
What is the energy of one quantum of
this energy?
E = hv
= 6.63 x 10-34 J-s(4.69 x 1014 s-1)
Prof. J. T. Spencer
CHE
106
What is Quantization
22
Sample exercise: A laser emits light
with a frequency of 4.69 x 1014 s-1.
What is the energy of one quantum of
this energy?
E = hv
= 6.63 x 10-34 J-s(4.69 x 1014 s-1)
= 3.11 x 10-19 J
Prof. J. T. Spencer
CHE
106
What is Quantization
23
Sample exercise: The laser emits its
energy in pulses of short duration. If
the laser emits 1.3 x 10-2 J of energy
during a pulse, how many quanta of
energy are emitted during the pulse?
Prof. J. T. Spencer
CHE
106
What is Quantization
24
Sample exercise: The laser emits its
energy in pulses of short duration. If
the laser emits 1.3 x 10-2 J of energy
during a pulse, how many quanta of
energy are emitted during the pulse?
1.3 x 10-2 J
Prof. J. T. Spencer
CHE
106
What is Quantization
25
Sample exercise: The laser emits its
energy in pulses of short duration. If
the laser emits 1.3 x 10-2 J of energy
during a pulse, how many quanta of
energy are emitted during the pulse?
1.3 x 10-2 J
Prof. J. T. Spencer
1 quatum
3.11 x 10-19 J
CHE
106
What is Quantization
26
Sample exercise: The laser emits its
energy in pulses of short duration. If
the laser emits 1.3 x 10-2 J of energy
during a pulse, how many quanta of
energy are emitted during the pulse?
1.3 x 10-2 J
1 quatum
3.11 x 10-19 J
= 4.2 x 1016 quanta
Prof. J. T. Spencer
CHE
106
Albert Einstein
27
Photoelectric Effect
Relativity
Nuclear Nonproliferation
Nobel Prize
(1879-1955)
Prof. J. T. Spencer
CHE
106
Photoelectric Effect
28
Vacuum Tube
light
metal
metal
electrons
Voltage Source
Prof. J. T. Spencer
Current
Meter
CHE
106
Wave Properties of Matter

De Broglie - particles behave under some
circumstances as if they are waves (just as light
behaves as particles under some circumstances).
Determines relationship:  = h/mv
 = wavelength
h = Planck’s const.
m = mass
v = velocity

Particle
electron
He atom (a)
Baseball
fast ball
slow ball
Prof. J. T. Spencer
mass (kg)
9 x 10-31
7 x 10-27
v (m/sec)
1 x 105
1000
 (pm)
7000
90
0.1
0.1
20
0.1
3 x 10-22
7 x 10-20
CHE
106
29
Niels Bohr (Denmark)




30
Built upon Planck,
Einstein and others
work to propose
explanation of line
spectra and atomic
structure.
Nobel Prize 1922
Worked on Manhatten
Project
Advocate for peaceful
nuclear applications
Prof. J. T. Spencer
CHE
106
Bohr’s Model

31
Continuous Spectra vs. Line Spectra
Wave-like
Behavior
Sunlight
Wave-like
Behavior
Hydrogen
Dispersion by Prism
Prof. J. T. Spencer
Dispersion by Prism
CHE
106
Red
Blue
32
364.6 nm
410.2 nm
434.0 nm
486.1 nm
656.3 nm
Hydrogen Emission
Ultraviolet
A Swiss schoolteacher in 1885 (J. Balmer) derived
a simple formula to calculate the wavelengths of
the emission lines (purely a mathematical feat
with no understanding of why this formula
worked)
frequency = C ( 1 - 1 ) where n = 1, 2, 3, etc...
22 n2 C = constant
Prof. J. T. Spencer
CHE
106
Bohr’s Model
33
“Microscopic Solar Syatem”



Electrons in circular
orbits around nucleus
with quantized (allowed)
energy states
When in a state, no energy
is radiated but when it
changes states, energy is
emmitted or gained equal
to the energy difference
between the states
Emission from higher to
lower, absorption from
lower to higher
Prof. J. T. Spencer
n=œ
n=4
n=3
n=2
electronic
transitions
n=1
CHE
106
Bohr’s Model
34
“Microscopic Solar Syatem”




The electrons in these
orbits have certain
specific radii, and
represent an energy
which fits a mathematical
formula
En = (-RH)(1/n2)
RH is the Rydberg
constant
The integer n is equal to
the principal quantum
number
Prof. J. T. Spencer
n=œ
n=4
n=3
n=2
electronic
transitions
n=1
CHE
106
Bohr’s Model
35
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state. In what
portion of the electromagnetic
spectrum is this line found?
Prof. J. T. Spencer
CHE
106
Bohr’s Model
36
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = DE = RH 1 _ 1
2
h
h in 2
n
f
Prof. J. T. Spencer
CHE
106
Bohr’s Model
37
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = DE = 2.18 x 10-18 J 1 _ 1
2
h 6.63 x 10-34 J-s in2
n
f
Prof. J. T. Spencer
CHE
106
Bohr’s Model
38
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = DE = 2.18 x 10-18 J 1 _ 1
h 6.63 x 10-34 J-s 32
12
Prof. J. T. Spencer
CHE
106
Bohr’s Model
39
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = DE = 2.18 x 10-18 J 1 _ 1
h 6.63 x 10-34 J-s 32
12
= (3.29 x 1015 s-1)(-0.889)
Prof. J. T. Spencer
CHE
106
Bohr’s Model
40
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = DE = 2.18 x 10-18 J 1 _ 1
h 6.63 x 10-34 J-s 32
12
= (3.29 x 1015 s-1)(-0.889)
= -2.92 x 1015 s-1
Prof. J. T. Spencer
CHE
106
Bohr’s Model
41
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = -2.92 x 1015 s-1
c = v
Prof. J. T. Spencer
CHE
106
Bohr’s Model
42
“Microscopic Solar Syatem”
Sample exercise: Calculate the
wavelength of hydrogen emission
line that corresponds to the
transition of the electron from the
n=3 to the n=1 state.
v = -2.92 x 1015 s-1
c = v
3.00 x 108 m/s = (2.92 x 1015 s-1)x
 = 1.03 x 10-7 m = 103 nm
Prof. J. T. Spencer
CHE
106
Bohr’s Model
43
“Microscopic Solar Syatem”
Sample exercise: In what portion of
the electromagnetic spectrum is
this line found?
 = 1.03 x 10-7 m = 103 nm
Prof. J. T. Spencer
CHE
106
Bohr’s Model
44
“Microscopic Solar Syatem”
Sample exercise: In what portion of
the electromagnetic spectrum is
this line found?
 = 1.03 x 10-7 m = 103 nm
ultraviolet range
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
45
Louis de Broglie boldly extended the idea of
energy having dual properties:
if energy can have dual properties, so can
matter.
the characteristic wavelength of any particle
of matter depends on its mass
 = h
mv
the wavelength for most objects is so small it
is not observable, only on an atomic scale will
matter waves be important
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
46
Sample exercise: At what velocity
must a neutron be moving in order
for it to exhibit a wavelength of
500 pm?
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
47
Sample exercise: At what velocity
must a neutron be moving in order
for it to exhibit a wavelength of
500 pm?
= h
mv
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
48
Sample exercise: At what velocity
must a neutron be moving in order
for it to exhibit a wavelength of
500 pm?
= h
mv
Prof. J. T. Spencer
5.00 x 10-10 m = 6.63 x 10-34 J-s
(1.67 x 10-27 kg)x
CHE
106
Wave Behavior of Matter
49
Sample exercise: At what velocity must a
neutron be moving in order for it to
exhibit a wavelength of 500 pm?
= h
mv
5.00 x 10-10 m = 6.63 x 10-34 J-s
(1.67 x 10-27 kg)x
(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
50
Sample exercise: At what velocity must a
neutron be moving in order for it to
exhibit a wavelength of 500 pm?
(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s
x=
6.63 x 10-34 J-s
5.00 x 10-10 m)(1.67 x 10-27 kg)
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
51
Sample exercise: At what velocity must a
neutron be moving in order for it to
exhibit a wavelength of 500 pm?
(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s
x=
6.63 x 10-34 (kg/m2-s2)s
5.00 x 10-10 m)(1.67 x 10-27 kg)
Prof. J. T. Spencer
CHE
106
Wave Behavior of Matter
52
Sample exercise: At what velocity must a
neutron be moving in order for it to
exhibit a wavelength of 500 pm?
(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s
x=
6.63 x 10-34 (kg*m2/s2)s
5.00 x 10-10 m)(1.67 x 10-27 kg)
x = 7.94 x 102 m/s
Prof. J. T. Spencer
CHE
106
Principle Quantum
Number





53
Each orbit corresponds to a different value of n
The radius of the orbit gets larger as the n value
increases
First allowed energy level is n = 1, then n=2 and
so on
Radius of orbital for n = 1 is 0.529 angstroms, the
2nd energy level is 22 or 4 times larger, n=3
would be 32 or 9 times larger and so on
If all electrons are in lowest energy this is
the GROUND STATE
Prof. J. T. Spencer
CHE
106
Uncertainty Principle



For a macroscopic particle, “classical”
mechanics (Newtonian) says that the position,
direction and velocity of the particle may be
determined exactly.
Since particles also have wave-like properties
and waves continue to an undefined location in
space, is it really possible to exactly determine
the position, direction and velocity of a particle
exactly?
Werner Heisenberg (1901-1976) concluded that
the duality of nature limits how precisely we can
know the location and momentum of a particle.
UNCERTAINTY PRINCIPLE
Prof. J. T. Spencer
CHE
106
54
Werner Heisenberg
Uncertainty Principle
Quantum Mechanics
Became Full Professor at
25 yrs.
Nobel Prize at 32
(1901-1976)
Prof. J. T. Spencer
CHE
106
55
Uncertainty Principle

56
Consider: determine exactly the position and
velocity (or momentum) of an atomic particle (i.e.,
an electron - a very small item).
– To “see” the particle, light (photons) must
bounce off it to be detected by our eyes and
thus allow is to measure its position.
– BUT, in the interaction of light with the
particle some energy is transferred to the
particle changing it velocity (or momentum).
– Thus, the act of measurement affects what we
are measuring.
– Heisenberg - (Dx) (Dmv) •h/4
Prof. J. T. Spencer
CHE
106
Uncertainty Principle
57
Very Fast Shutter Speed - can determine position
very accurately but cannot determine direction or
speed very accurately
Very Slow Shutter Speed - can determine direction
very accurately but cannot determine position very
accurately
Prof. J. T. Spencer
CHE
106
Duality of Nature
58
Uncertainty principle says that the
position and momentum of a particle (such
as an electron) cannot be exactly
determined. Thus, how can we
understand an electron’s “actions” in an
atom?
 How can the two seemingly very different
properties (wave-like and particulate) of
light and matter be possible? How does
quantization of energy and matter fit into
the picture?

Prof. J. T. Spencer
CHE
106
Erwin Schrödinger
59
Quantum Mechanics
Erwin Schrödinger
(1887-1961) developed a
new way of dealing
with this dual nature Quantum Mechanics.
(1887-1961)
Prof. J. T. Spencer
CHE
106
60
Prof. J. T. Spencer
CHE
106
Quantum Mechanics

61
Schrödinger - starts with the measurable
energies of atoms and works towards the
description of the atom, basically solving the
problem backwards.
– Wave equation - equation used to describe
the wave properties of an electron. If you
understand all the features of the equation,
then you can know all that's possible about
the electron.
– solutions to the wave equation are called
wave functions () or orbitals - contain
information about the energy and electron’s
3D position in space (probability).
Prof. J. T. Spencer
CHE
106
Wave Equation
62
n=1
n=2
n=3
Prof. J. T. Spencer
“Stable” solution to
the jump-rope wave
equation
CHE
106
Quantum Mechanics

63
Wave functions () are without physical meaning
BUT 2 gives the probability of finding an
electron within a given region of space.
Wave
Equation
s
o
l
v
e
Wave
function or
Orbital ()
Probability of
finding an
electron
within a
region of
space ()
How does an electron get from position A to Position B?
The question is unanswerable since it assumes particle
behavior of electron and NOT wave properties.
Prof. J. T. Spencer
CHE
106
Probability (2)
64
Orbital (2) - a region of
space within which there is
a certain probability of
finding the electron.
similar to a baseball
field; there is a certain
probability of finding
the baseball during a
game within the park
and a higher
probability of finding
it in the infield than in
the outfield. A ball can
be hit over the fence
which is equivalent to
electron ionization.
Prof. J. T. Spencer
V
i
s
i
t
o
r
s
Home
CHE
106
Probability (2)
probability
of finding
the baseball
during the
game
pitcher’s mound
infield
warning track
65
Plot of
Probabilitynce
increases.
home run
distance from home plate
Prof. J. T. Spencer
CHE
106
Probability (2)
Orbital is a region of high probability of finding
the electron (no trajectory/path information)
1 D Plot (probability and distance
measured along red arrow)
66
1s
3D Plot (spherical surface
within which the electron
spends x% of its time)
2
Prob. of
finding
the
electron
distance from nucleus
Prof. J. T. Spencer
2D Contour Plot (lines
within which the electron
spends x% of its time)
CHE
106
Orbitals



67
Probability or Electron Density - probability of
finding the electron at a particular location.
Regions with a high probability of finding the
electron have a high electron density.
Orbitals - solutions to the wave equation - have
specific energies and probability profiles. (orbitals
have characteristic shapes and energies).
– Orbit (orbit implies pathway) - Bohr models uses
1 quantum value (n) to describe the orbit
Quantum Numbers - (from wave equation) each
orbital) has 3 quantum numbers.
– describe shapes and energies of orbitals.
– accounts for quantized (allowed) energies.
Prof. J. T. Spencer
CHE
106
Quantum Numbers (QN)



68
Principal Quantum Number (n ) - may have
integral values >0 (i.e., 1, 2, 3, 4,...). Dictates the
size and energy level of an orbital As n increases
both the size and energy of the orbital increases.
Angular Momentum Azimuthal) Quantum
Number (l ) - may have values from 0 to (n-1).
Defines the 3D shape of the orbital. Often
referred to by letter (i.e., l = 0 = s, l = 1 = p, etc...)
When more than 1 electron exists, the l Q.N. also
describes energy.
Magnetic Quantum Number (ml ) - may have
values of -l to +l. Defines the spatial orientation
of the orbital along a standard coordinate axis
system.
Prof. J. T. Spencer
CHE
106
Quantum Numbers (QN)


69
Collection of orbitals with the same n Q.N. value
is called an electron shell or principal energy
level.
Collection of orbitals with the same n and l
values is called an electron subshell.
– Each shell is divided into subshells equal to
the principal quantum number (n)
– Each subshell is divided into orbitals
n
l subshell ml spatial orient.
1
0
s
0
2
1
p
1, 0, -1
3
2
d
2, 1, 0, -1, -2
4
3
f
3, 2, 1, 0, -1, -2, -3
Prof. J. T. Spencer
CHE
106
Quantum Number/Address

70
Quantum numbers may be thought of as energy
and space addresses.
Quantum Number Address
n
building
l
ml
Prof. J. T. Spencer
floor
room
CHE
106
Quantum Numbers

Combinations of the quantum numbers specifies
which specific electron we are referring to in an
atom (address)
n
l
1
2
0
0
1
0
1
2
3
71
subshell
1s
2s
2p
3s
3p
3d
Prof. J. T. Spencer
ml
0
0
1, 0, -1
0
1, 0, -1
2, 1, 0, -1, -2
no. of orbs no. of e-l
1
1
3
1
3
5
2
2
6
2
6
10
2
8
18
CHE
106
Quantum Numbers

72
Quantum Numbers also specify energy of the
occupying electrons,
0
E
N
E
R
G
Y
n=•
n=4
n=3
n=2
n=1
Prof. J. T. Spencer
l=0
4s
3s
2s
1s
l=1
4p
3p
l=2
4d
3d
l=3
4f
2+6+10+14
=32
electrons
2p
max
2+6+10=18
electrons
max
2+6=8
electrons
max
2
electrons
max
CHE
106
Quantum Number/Address
73
Sample exercises: What is the
designation for the subshell with n=5
and l = 1?
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
74
Sample exercises: What is the
designation for the subshell with n=5
and l = 1?
n = 5 is 5th principle energy level
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
75
Sample exercises: What is the
designation for the subshell with n=5
and l = 1?
n = 5 is 5th principle energy level
l = 1 is the p subshell
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
76
Sample exercises: What is the
designation for the subshell with n=5
and l = 1? How many orbitals are in
this subshell?
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
77
Sample exercises: What is the
designation for the subshell with n=5
and l = 1? How many orbitals are in
this subshell?
p subshell has 3 orbitals
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
78
Sample exercises: What is the
designation for the subshell with n=5
and l = 1? How many orbitals are in
this subshell? Indicate the values of
ml for each of these orbitals.
Prof. J. T. Spencer
CHE
106
Quantum Number/Address
79
Sample exercises: What is the
designation for the subshell with n=5
and l = 1? How many orbitals are in
this subshell? Indicate the values of
ml for each of these orbitals.
p subshell has 3 orbitals, labeled
-1, 0, 1
Prof. J. T. Spencer
CHE
106
Orbitals



80
Ground state - when an electron is in the lowest
energy orbital.
Excited state - when an electron is in another
orbital.
All orbitals of the same l values are the same
shape (different relative sizes and energies).
1s
Prof. J. T. Spencer
2s
3s
CHE
106
l=0
s Orbitals
81
Boundary Plots (angular)
Radial Plots
Nodes
Node
2
(1s)
2
(2s)
1s
2
(3s)
2s
radius
radius
3s
radius
Node - where 2 goes to zero
Prof. J. T. Spencer
CHE
106
82
2s
Prof. J. T. Spencer
3s
CHE
106
l=1
p Orbitals
2pz
Prof. J. T. Spencer
83
3px
CHE
106
p Orbitals
l=1
y
y
y
z
py
px
x
2p
x
z
pz
z
x
x
y
z
84
2
(p)
Radial Electron
Distribution
3p
radius
Prof. J. T. Spencer
CHE
106
d orbitals
l=2
dz2
Prof. J. T. Spencer
85
dx2-y2
CHE
106
d orbitals
l=2
dxy
y
dx2-y2
z
y
dyz
y
z
x
Prof. J. T. Spencer
dz2
z
x
86
y
z
x
orbital shapes
are approx. the
same for each l
value except for
their relative
sizes (and
energies).
x
dxz
y
z
x
CHE
106
Many Electron Atoms




87
Wave equation solved for only the smallest
atoms (very intensive calculations). Larger
atoms calculated by approximations.
Shapes of orbitals for larger atoms (>H) are
essentially the same as those found for
hydrogen.
The energies of the orbitals are, however,
significantly changed in many electron
systems.
For H, the energy of an orbital depends only
on n, while for larger atoms, the l value also
affects energy levels due to
electron-electron repulsions.
Prof. J. T. Spencer
CHE
106
Many Electron Atoms
0
n=1
n=2
n=3
3d
n=4
4p
4s
88
n=5
5s
3p
E
N
E
R
G
Y
3s
2p
2s
s (l = 0)
p (l = 1)
d (l = 2)
1s
Prof. J. T. Spencer
CHE
106
Effective Nuclear Charge



In many electron atoms, electron-electron
repulsions (besides electron-nuclear attractions)
become important.
Estimate the energy of an electron in an orbital
by considering how it, on the average, interacts
with its electronic environment (treat electrons
individually).
The net attractive force that an electron will feel
is the effective nuclear charge (Zeff).
89
Z = nuclear charge
S = screening value

Zeff = Z - S
Screening is the average number of other
electrons that are between the electron and the
nucleus.
Prof. J. T. Spencer
CHE
106
Effective Nuclear Charge
Zeff = Z - S
Average electronic
charge (S) between
the nucleus and the
electron of interest
r
Z
Prof. J. T. Spencer
90
The larger
the Zeff an
electron feels
leads to a
lower energy
for the
electron
Electrons outside of sphere of
radius r have very little effect on
the effective nuclear charge
experienced by the electron at
radius r
CHE
106
Shielding (Screening Effect)
“Football”
91
Screening effect (at the ball snap!):
X X
X
X
QB
X
X
X X X X X
11
Defensive
Players
Prof. J. T. Spencer
– the offensive linemen can
screen one defensive
player completely (they
spend all of their time in
front of the quarterback).
– the half backs, since they
are further back, can only
partially screen out a
defensive player.
– the fullbacks are behind
the QB and can’t screen
out any defensive players.
CHE
106
Screening


92
For a given n value, the Zeff decreases with
increasing values of l (screening ability; s>p>d>f).
For a given n value, the energy of an orbital
increases with increasing values of l.
2
s electrons spend more
time near the nucleus than
do the p electrons (and
p>d). Thus s electrons
shield better than p and p
better than d.
3s
3p
3d
radius
Prof. J. T. Spencer
CHE
106
Screening
93
Sample exercise: The sodium atom
has 11 electrons. Two occupy a 1s
orbital, two occupy a 2s orbital, and
one occupies a 3s orbital. Which of
these s electrons experiences the
smallest effective nuclear charge?
Prof. J. T. Spencer
CHE
106
Screening
94
Sample exercise: The sodium atom
has 11 electrons. Two occupy a 1s
orbital, two occupy a 2s orbital, and
one occupies a 3s orbital. Which of
these s electrons experiences the
smallest effective nuclear charge?
3s electrons are farthest from
the nucleus and shielded.
Prof. J. T. Spencer
CHE
106
Electron Spin

95
Electrons have spin properties (spin along axis).
N
-
-
N
Electron spin is
quantized
ms = + 1/2 or - 1/2
Magnetic Fields
Prof. J. T. Spencer
CHE
106
Experimental Electron Spin


96
Passing an atomic beam (neutral atoms) which
contained an odd number of electrons (1 unpaired
electron, see later) through a magnetic field caused
the beam to split into two spots.
Showed the possible states of the single (unpaired)
electron as quantized into ms = +1/2 or - 1/2.
two
Atom
Beam
Generator
Slits
Magnetic
Field
N
Viewing
Screen
electron
spin
states
S
Prof. J. T. Spencer
CHE
106
Nuclear Spin

97
Like electrons, nuclei spin and because of this
spinning of a charged particle (positively
charged), it generates a magnetic field. Two
states are possible for the proton (1H).
N
S
+
+
S
N
Prof. J. T. Spencer
CHE
106
Nuclear Spin
Similar to a canoe paddling
either upstream or
downstream
98
S
Antiparallel
Degenerate
DE
N
N
N
S
Parallel
S
N
S
External Magnetic Field
Prof. J. T. Spencer
CHE
106
Magnetic Resonance
Imaging MRI





99
Hydrogen atom has two nuclear spin quantum
numbers possible (+1/2 and -1/2).
When placed in an external magnetic field, 1H can
either align with the field (“parallel” - lower
energy) or against the field (“antiparallel” - higher
energy).
Energy added (DE) can raise the energy level of an
electron from parallel to antiparallel orientation
(by absorbing radio frequency irradiation).
Electrons (also “magnets”) in “neighborhood” affect
the value of DE (i.e., rocks in stream).
By detecting the DE values as a function of position
within a body, an image of a body’s hydrogen atoms
may be obtained.
Prof. J. T. Spencer
CHE
106
MRI


Advantages
– non-invasive.
– no ionizing or other “dangerous” radiation
(such as X-rays of positrons).
– Can be done frequently to monitor progress of
treatment.
– images soft tissues (only those with hydrogen
atoms (almost all “soft” tissues).
– images function through the use of contrast
media.
Disadvantages
– Relatively expensive equipment
Prof. J. T. Spencer
CHE
106
100
MRI; Hardware
Prof. J. T. Spencer
101
CHE
106
MRI
Prof. J. T. Spencer
102
CHE
106
MRI
Prof. J. T. Spencer
103
CHE
106
MRI
Prof. J. T. Spencer
104
CHE
106
MRI
Prof. J. T. Spencer
105
CHE
106
MRI
Prof. J. T. Spencer
106
CHE
106
Wolfgang Pauli
107
1900-1958



Prof. J. T. Spencer
explained the electron
spin experiments in
terms of quantum
mechanics
Austrian Physicist who
explained that no
electrons in an atom may
occupy the same
quantum state .....Have
the same four quantum
numbers
1945 Nobel Prize for
Exclusion Principle
CHE
106
Pauli Exclusion Principle


108
Pauli exclusion principle - no two electrons in an
atoms can have the same set of four quantum
numbers (n, l, ml, ms).
For a given orbital, n, l, and ml are set but each
orbital can hold 2 electrons with opposite ms
values (ms = +1/2 and -1/2).
Energy
1s
2s
= an electron with ms
Prof. J. T. Spencer
2px
= +1/2
2py
2pz
= an electron with ms
= -1/2
CHE
106
Electron Configurations


109
Fill orbitals with electrons STARTING at lowest
energy (ground state configuration). [just as
filling a glass with water starts at the bottom and
fills up.
No more that two electrons per orbital (Pauli).
Orbital Diagram
Paired Electrons
Unpaired Electron
1s
Written
2s
2px
2py
2pz
Energy
1s22s12p0 etc...
Prof. J. T. Spencer
CHE
106
Electron Configurations
0
E
N
E
R
G
Y
n=1
n=2
fill orbitals with
electrons from
lowest to highest
energy (bottom to
top) just as if
filling a glass with
water
2p
n=3
3d
3p
3s
n=4
4p
4s
110
n=5
5s
s (l = 0)
p (l = 1)
d (l = 2)
2s
1s
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 etc...
Prof. J. T. Spencer
CHE
106
Electronic Configurations
Orbital Diagram
111
Energy
Degenerate Orbitals
5B
Degenerate Orbitals
1s2 2s2 2p0
6C
1s2 2s2 2p1
6C
1s2 2s2 2p2
6C
What do we do with Carbons 2 p electrons?
1s
2s
Prof. J. T. Spencer
2px
2py
2pz
3s
3px
3py
3pz
CHE
106
Hund’s Rule
Orbital Diagram
1s
Energy
2s
Where does the
next electron go?

112
2px
2py
2pz
Degenerate Orbitals (all at
the same energy)
Hund’s rule (of maximum multiplicity) - the lowest
energy configuration for an atom is the one
having the maximum number of unpaired
electrons allowed by the Pauli exclusion principle
in a given set of degenerate orbitals (group of
orbitals with the same energy) with all
unpairedaving parallel spins.
Prof. J. T. Spencer
CHE
106
Electronic Configurations
Orbital Diagram
113
Energy
Degenerate Orbitals
3Li
Degenerate Orbitals
1s2 2s1 2p0
4Be
1s2 2s2 2p0
5B
1s2 2s2 2p1
6C
1s2 2s2 2p2
7N
1s2 2s2 2p3
1s
2s
Prof. J. T. Spencer
2px
2py
2pz
3s
3px
3py
3pz
CHE
106
Electronic Configurations
Orbital Diagram
114
Energy
8O
1s2 2s2 2p4
9F
1s2 2s2 2p5
10Ne
1s2 2s2 2p6
11Na
1s2 2s2 2p63s1
12Mg
1s2 2s2 2p6 3s2
1s
2s
Prof. J. T. Spencer
2px
2py
2pz
3s
3px
3py
3pz
CHE
106
Electronic Configurations




115
Electron Configurations:
– Obey Pauli Exclusion Principle
– Obey Hund’s rule (where applicable)
– Fill from lowest to highest energies
– Shorthand;
» 11Na: [Ne] 3s1 equivalent to 1s2 2s2 2p6 3s1
» 19K: [Ar] 4s1 equivalent to 1s2 2s2 2p6 3s2 3p6 4s1
Closed shell (filled), half filled, and empty orbital
configurations most stable.
Outer electrons (max. n for atom) are valence elec.
Inner electrons (not max. n for atom) are core elec.
Prof. J. T. Spencer
CHE
106
Electronic Configurations

116
Transition elements (metals) fill d orbitals.
22Ti
[Ar] 4s2 3d2
23V
[Ar] 4s2 3d3
24Cr
[Ar] 4s1 3d5
25Mn
[Ar] 4s2 3d5
29Cu
[Ar] 4s1 3d10
4s
3d
Prof. J. T. Spencer
3d
3d
3d
3d
4p
4p
4p
CHE
106
Periodic Table
2
1
3
1H
3 Li
4
6
5
s orbitals
p orbitals
2s Be
11
10
9
f orbitals
8
7
12
12 M g
19 K
20 Ca
21 Sc
22 Ti
23 V
24 Cr
25 M n
37 Rb
38 Sr
39 Y
40 Zr
41 Nb
42 M o
73 Ta
3s
55 Cs
56
57 La
72 Hf
87
88
89 Ac
104 Unq 105 Unp
6s Ba
Fr7s Ra
14
15
16
18
5B
6C
7N
2p
8O
9F
10 Ne
13 Al
14 Si
15 P
3p
16 S
17 Cl
18 Ar
3dFe
26
27 Co
28 Ni
29 Cu
30 Zn
31 Ga
32 Ge
33 As
4p
34 Se
35 Br
36 Kr
43 Tc
4dRu
45 Rh
46 Pd
47 Ag
48 Cd
49 In
50 Sn
51 Sb
5p
52 Te
53 I
54 Xe
74 W
75 Re
5dOs
77 Ir
78 Pt
79 Au
80 Hg
81 Tl
82 Pb
83 Bi
6p
84 Po
85 At
86 Rn
106 Unh
107 Ns
6d Hs
108
109 M t
70 Yb
71 Lu
44
76
58 Ce
59 Pr
60 Nd
61 Pm
62 Sm
63 Eu
64 Gd
65 Tb
66 Dy
67 Ho
68 Er
69 Tm
90 Th
91 Pa
92 U
93 Np
94 Pu
95 Am 96 Cm
97 Bk
98 Cf
99 Es
100 Fm
101 Md 102 No
Prof. J. T. Spencer
17
2 He
d orbitals
11 Na
5s
13
closed shell
4
4s
117
4f
5f
103 Lr
CHE
106
Cations


118
To determinens (usually the last one added).
EXCEPT for transition metal ions - which have
NO n(max)s electrons.
25Mn
25Mn+1
4s
Prof. J. T. Spencer
3d
3d
3d
3d
3d
4p
4p
4p
CHE
106
Electronic Configurations
119
Sample exercise: What family of
elements is characterized by having an
ns2p2 outer-electron configuration?
Prof. J. T. Spencer
CHE
106
Electronic Configurations
120
Sample exercise: What family of
elements is characterized by having an
ns2p2 outer-electron configuration?
2 + 2 = 4 valence electrons, so this is
Group IVA, or Group 14.
Prof. J. T. Spencer
CHE
106
Electronic Configurations
121
Sample exercise: Use the periodic table
to write the electron configurations for
the following atoms by giving the
appropriate noble-gas inner core plus
the electrons beyond it:
Co
Te
Prof. J. T. Spencer
CHE
106
Electronic Configurations
122
Sample exercise: Use the periodic table
to write the electron configurations for
the following atoms by giving the
appropriate noble-gas inner core plus
the electrons beyond it:
Co : [Ar]4s23d7
Te
Prof. J. T. Spencer
CHE
106
Electronic Configurations
123
Sample exercise: Use the periodic table
to write the electron configurations for
the following atoms by giving the
appropriate noble-gas inner core plus
the electrons beyond it:
Co : [Ar]4s23d7
Te: [Kr]5s24d105p4
Prof. J. T. Spencer
CHE
106
End Chapter Six









Duality of Nature (wave-like and particulate
properties), DeBroglie
Quantization and the Schrödinger Equation
Heisenberg Uncertainty Principle
Atomic Orbitals and Wave Functions (solutions to
Wave Equation).
Quantum Numbers
Orbital Energies, Shapes, Nodes
Multi-electron Atoms, Screening and Zeff
Pauli Exclusion Principle
Hund’s Rule of Maximum Multiplicity
Continued
Prof. J. T. Spencer
CHE
106
124
Chapter Six (Con’t)




125
Electron Spin
Nuclear Spin (MRI)
Electronic Configurations
Periodic Table and orbital filling
Prof. J. T. Spencer
CHE
106