Download Chapter 8 CHEM 161

CHEMISTRY
The Molecular Nature of Matter
SIXTH EDITION
Jespersen • Brady • Hyslop
Chapter 8
The Quantum Mechanical Atom
Copyright © 2012 by John Wiley & Sons, Inc.
The nature of Light
Electromagnetic Radiation
 Light: Energy transferred between atoms/molecules
 Travels through space at high speed in vacuum
 c = speed of light = 2.9979 × 108 m/s
 Light is radiation that carries energy through space
by means of waves.
Waves or Oscillations
 Systematic fluctuations in intensities of electrical
and magnetic forces
 Varies regularly with time
 ExhibitJespersen/Brady/Hyslop
wide range of
energy
Chemistry:
The Molecular Nature of Matter, 6E
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Properties of Waves
Wavelength ()
 Distance between two successive peaks or troughs
 Units are in meters, centimeters, nanometers
Frequency ()
 Number of waves per second that pass a given point in
space
 Units are in Hertz (Hz = cycles/sec = 1/sec = s–1)
Related by
=c
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Properties of Waves
Amplitude
 Maximum and minimum height
 Intensity of wave, or brightness
 Varies with time as travels through space
Nodes
 Points of zero amplitude
 Place where wave goes through axis
 Distance between nodes is constant
nodes
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Learning Check: Converting from
Wavelength to Frequency
The bright red color in fireworks is due to emission
of light when Sr(NO3)2 is heated. If the
wavelength is ~650 nm, what is the frequency of
this light?
8
c 3.00 ´ 10 m/s
n= =
l
650 ´ 10-9 m
 = 4.61 × 1014 s–1 = 4.6 × 1014 Hz
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Your Turn!
WCBS broadcasts at a frequency of 880 kHz.
What is the wavelength of their signal?
A. 341 m
B. 293 m
C. 293 mm
D. 341 km
c 3.00 ´ 108 m/s
l= =
3
n
880 ´ 10 / s
E. 293 mm
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Electromagnetic Spectrum
 Comprised of all frequencies of light
 Divided into regions according to wavelengths
of radiation
high energy, short waves
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low energy, long waves
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Electromagnetic Spectrum
Visible light
 Band of wavelengths that human eyes can see
 400 to 700 nm
 Make up spectrum of colors
White light
 Combination of all these colors
 Can separate white light into the colors with a prism
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Important Experiments in Atomic Theory
Late 1800’s:
 Matter and energy believed to be distinct
 Matter: made up of particles
 Energy: light waves
Beginning of 1900’s:
 Several experiments proved this idea incorrect
 Experiments showed that electrons acted like:
 Tiny charged particles in some experiments
 Waves in other experiments
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Photosynthesis
 If you irradiate plants with infrared and microwave
radiation
 No photosynthesis
 Regardless of light intensity
 If you irradiate plants with visible light
 Photosynthesis occurs
 More intense light now means more photosynthesis
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Line Spectrum
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Particle Theory of Light
 Max Planck and Albert Einstein (1905)
 Electromagnetic radiation is stream of small packets
of energy
 Quanta of energy or photons
 Each photon travels with velocity = c
 Waves with frequency = 
 Energy of photon of electromagnetic radiation is
proportional to its frequency
 Energy of photon E = h 
 h = Planck’s constant
= 6.626 × 10–34 J s
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Atomic Spectra
 Atomic line spectra are rather complicated
 Line spectrum of hydrogen is simplest
 Single electron
 First success in explaining quantized line spectra
 First studied extensively
 J.J. Balmer
 Found empirical equation to fit lines in visible
region of spectrum
 J. Rydberg
 More general equation explains all emission lines in
H atom spectrum (infrared, visible, and UV)
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Rydberg Equation
 1

1
1
 RH  2  2 
n


n
2 
 1
RH = 109,678 cm–1 = Rydberg constant
 = wavelength of light emitted
n1 and n2 = whole numbers (integers) from 1 to 
where n2 > n1
If n1 = 1, then n2 = 2, 3, 4, …
 Can be used to calculate all spectral lines of
hydrogen
 The values for n correspond to allowed energy levels
for atom
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Learning Check: Using Rydberg
Equation
Consider n1 = 2 Calculate  (in nm) for the
transition from n2 = 6 down to n1 = 2.
æ1 1ö
æ
1ö
-1 1
= RH çç 2 - 2 ÷÷ = 109,678 cm çç - ÷÷ = 24,373 cm–1
l
è2 6 ø
è 4 36 ø
1
l=
1
-5
-1
24,372.9 cm
 = 410.3 nm
= 4.1029 ´ 10
1m
1 nm
cm ´
´
100 cm 1 ´ 10-9 m
Violet line in spectrum
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Learning Check
A photon undergoes a transition from nhigher down to n = 2
and the emitted light has a wavelength of 650.5 nm?
1 ´ 10-7 cm
-7
l = 650.5 nm ´
= 650.5 ´10 cm
1 nm
-1 1
1
1 )
=
109,678
cm
(
650.5 ´ 10-7 cm
22 (n )2
2
1
=(1 - 12 )
7.13455
4 (n2 )
1 =11
= 0.110
2
(n2 ) 4 7.13455
(n )
n2 = 3
2
2
1
=
= 9.10
0.110
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Your Turn!
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?
A. 1.28 × 103 nm
B. 1.462 × 104 nm
C. 7.80 × 102 nm
D. 7.80 × 10–4 nm
E. 3.65 × 10–7 nm
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1
1 
1  1
 109 ,678 cm  2  2 

5 
3
1
 7799 cm1

1
1 ´ 107nm
l=
´
-1
1 cm
7799 cm
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Significance of Atomic Spectra
 Atomic line spectra tells us
 When excited atom loses energy
 Only fixed amounts of energy can be lost
 Only certain energy photons are emitted
 Electron restricted to certain fixed energy levels in
atoms
 Energy of electron is quantized
 Simple extension of Planck's Theory
 Any theory of atomic structure must account for
 Atomic spectra
 Quantization of energy levels in atom
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What Does Quantized Mean?
Potential Energy of Rabbit
 Energy is quantized if
only certain discrete
values are allowed
 Presence of
discontinuities makes
atomic emission
quantized
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Bohr Model of Atom
 First theoretical model of atom to successfully
account for Rydberg equation
 Quantization of energy in hydrogen atom
 Correctly explained atomic line spectra
 Proposed that electrons moved around nucleus
like planets move around sun
 Move in fixed paths or orbits
 Each orbit has fixed energy
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Energy for Bohr Model of H
 Equation for energy of electron in H atom
2
4
1
2p me
E µ- 2
b=
n
h2
 Ultimately b relates to RH by b = RHhc
 OR
RH hc
b
E =- 2 =- 2
n
n
 Where b = RHhc = 2.1788 × 10–18 J/atom
 Allowed values of n = 1, 2, 3, 4, …
 n = quantum number
 Used to identify orbit
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Energy Level Diagram for H Atom
 Absorption of
photon
 Electron raised to
higher energy level
 Emission of photon
 Electron falls to
lower energy level
 Energy levels are quantized
 Every time an electron drops from one
energy level to a lower energy level
 Same frequency photon is emitted
 Yields line spectra
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Bohr Model of Hydrogen Atom
 n=1
First Bohr orbit
 Most stable energy state equals the ground state
which is the lowest energy state
 Electron remains in lowest energy state unless
disturbed
How to change the energy of the atom?
 Add energy, as light (E = h) or other form.
 Electron raised to higher n orbit n = 2, 3, 4, … 
 Higher n orbits = excited states = less stable
 So electron quickly drops to lower energy orbit and
emits photon of energy equal to E between levels
E = Eh – El
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h = higher l = lower
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Your Turn!
In Bohr's atomic theory, when an electron moves
from one energy level to another energy level
more distant from the nucleus,
A. energy is emitted
B. energy is absorbed
C. no change in energy occurs
D. light is emitted
E. none of these
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Light Exhibits Interference
Constructive interference
 Waves “in-phase” lead to greater amplitude
 They add together
Destructive interference
 Waves “out-of-phase” lead to lower amplitude
 They cancel out
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Diffraction and Electrons
 Light
 Exhibits interference
 Has particle-like nature
 Electrons
 Known to be particles
 Also demonstrate interference
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Standing vs. Traveling Waves
Traveling wave
 Produced by wind on surfaces of lakes and oceans
Standing wave
 Produced when guitar string
is plucked
 Center of string vibrates
 Ends remain fixed
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Standing Wave on a Wire
 Integer number (n) of peaks and troughs is
required
 Wavelength is quantized:
 L is the length of the string
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l=
2L
n
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How Do We Describe an Electron?
 Has both wave-like and particle-like properties
 Energy of moving electron on a wire is E =½ mv 2
 Wavelength is related to the quantum number, n,
and the wire length:
2L
l=
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n
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Electron Has Quantized Energy
 Electron energy quantized
 Depends on integer n
 Energy level spacing
changes when positive
charge in nucleus changes
 Line spectra different for
each element
 Lowest energy allowed is
for n =1
 Energy cannot be zero, hence atom cannot collapse
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Wave Functions
Schrödinger’s equation
 Solutions give wave functions and energy levels of
electrons
Wave function
 Wave that corresponds to electron
 Called orbitals for electrons in atoms
Amplitude of wave function squared
 Can be related to probability of finding electron at
that given point
Nodes
 Regions where electrons will not be found
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Orbitals Characterized by Three
Quantum Numbers:
Quantum Numbers:
 Shorthand
 Describes characteristics of electron’s position
 Predicts its behavior
n = principal quantum number
 All orbitals with same n are in same shell
ℓ = secondary quantum number
 Divides shells into smaller groups called subshells
mℓ = magnetic quantum number
 Divides subshells into individual orbitals
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n = Principal Quantum Number
 Allowed values: positive integers from 1 to 
 n = 1, 2, 3, 4, 5, … 
 Determines:
E =-
 Size of orbital
Z 2RH hc
n2
 Total energy of orbital
 RHhc = 2.18 × 10–18 J/atom
 For given atom,
 Lower n = Lower (more negative) E
= More stable
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ℓ = Orbital Angular Momentum
Quantum Number or Secondary
Quantum Number
 Allowed values: 0, 1, 2, 3, 4, 5…(n – 1)
s, p, d, f, g, h
 Letters:
Orbital designation
nℓ
letter
 Possible values of ℓ depend on n
number
 n different values of ℓ for given n
 Determines
 Shape of orbital
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mℓ = Magnetic Quantum Number
 Allowed values: from –ℓ to 0 to +ℓ
 Ex. when ℓ=2 then mℓ can be
 –2, –1, 0, +1, +2
 Possible values of mℓ depend on ℓ
 There are 2ℓ+1 different values of mℓ for given ℓ
 Determines orientation of orbital in space
 To designate specific orbital, you need three
quantum numbers
 n , ℓ , mℓ
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Table 8.1 Summary of Relationships
Among the Quantum Numbers n, ℓ, and mℓ
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Orbitals of Many Electrons
Orbital
Designation
 Based on first two
quantum numbers
 Number for n
and letter for ℓ
 How many
electrons can go
in each orbital?
 Two electrons
 Need another
quantum number
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Spin Quantum Number, ms
 Arises out of behavior of
electron in magnetic field
 Electron acts like a top
 Spinning charge is like a
magnet
S
 Electron behave like tiny
magnets
 Leads to two possible
directions of electron spin Possible Values:
 Up and down
 North and south
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+½

Chemistry: The Molecular Nature of Matter, 6E
N
½

38
Number of Orbitals and Electrons in
the Orbitals
Jespersen/Brady/Hyslop
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Energy Level Diagram for Multi
Electron Atom/Ion
4f
6s
5p
4d
5s
4p
3d
4s
Energy
3p
3s
2p
2s
 How to put electrons into a
diagram?
 Need some rules
1s
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Pauli Exclusion Principle
 No two electrons in same atom can have same set
of all four quantum numbers (n, ℓ, mℓ , ms)
 Can only have two electrons per orbital
 Two electrons in same orbital must have opposite
spin
 Electrons are said to be paired
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Hund’s Rule
 If you have more than one orbital all at the same
energy
 Put one electron into each orbital with spins parallel
(all up) until all are half filled
 After orbitals are half full, pair up electrons
Why?
 Repulsion of electrons in same region of space
 Empirical observation based on magnetic
properties
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Know from Magnetic Properties
 Two electrons in same orbital have different spins
 Spins paired—diamagnetic
 Sample not attracted to magnetic field
 Magnetic effects tend to cancel each other
 Two electrons in different orbital with same spin
 Spins unpaired—paramagnetic
 Sample attracted to a magnetic field
 Magnetic effects add
 Measure extent of attraction
 Gives number of unpaired spins
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Your Turn!
Which of the following is a valid set of four
quantum numbers (n, ℓ, mℓ , ms)?
A. 3, 2, 3, +½
B. 3, 2, 1, 0
C. 3, 0, 0, –½
D. 3, 3, 0, +½
E. 0, –1, 0, –½
Jespersen/Brady/Hyslop
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Your Turn!
What is the maximum number of electrons
allowed in a set of 4p orbitals?
A. 14
B. 6
C. 0
D. 2
E. 10
Jespersen/Brady/Hyslop
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Ground State Electron
Arrangements
Electron Configurations
 Distribution of electrons among orbitals of atom
1. List subshells that contain electrons
2. Indicate their electron population with superscript
e.g. N is 1s 2 2s 2 2p 3
Orbital Diagrams
 Way to represent electrons in orbitals
1. Represent each orbital with circle (or line)
2. Use arrows to indicate spin of each electron
e.g. N is
1s
Jespersen/Brady/Hyslop
2s
2p
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Aufbau Principle
1
1s
2s
3s
4s
5s
6s
7s
8s
2
2p
3p
4p
5p
6p
7p
3
4
5
6
3d
4d 4f
5d 5f
6d
Jespersen/Brady/Hyslop
7
8
5g
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Aufbau Principle and Periodic Table
 Divided into regions of 2, 6, 10, and 14 columns
 This equals maximum number of electrons in s, p,
d, and f sublevels
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Sublevels and the Periodic Table
 Each row (period) represents different energy level
 Each region of chart represents different type of
sublevel
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Orbital Diagram and Electron
Configurations: e.g. N, Z = 7
4p
3d
4s
Energy
3p
3s
2p
Each arrow represents an electron
2s
1s 2 2s 2 2p 3
1s
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Chemistry: The Molecular Nature of Matter, 6E
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Orbital Diagram and Electron
Configurations: e.g. V, Z = 23
4p
3d
4s
Energy
3p
3s
2p
2s
Each arrow represents an electron
1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3
1s
Jespersen/Brady/Hyslop
Chemistry: The Molecular Nature of Matter, 6E
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Learning Check
Give electron configurations and orbital diagrams
for Na and As
6s
5p
4d
5s
4p
3d
4s
Energy
3p
3s
2p
2s
Na Z = 11
1s 2 2s 2 2p 6 3s 1
As Z = 33
1s
1s 22s 22p 63s 23p 64s 23d 104p 3
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Your Turn!
What is the correct ground state electron
configuration for Si?
A. 1s 22s 22p 63s 23p 6
B. 1s 22s 22p 63s 23p 4
C. 1s 22s 22p 62d 4
D. 1s 22s 22p 63s 23p 2
E. 1s 22s 22p 63s 13p 3
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Where Are The Electrons?
 Each box represents room for an electron.
 Read from left to right
n= 1 1
H
n= 2 3
“ns” orbital being filled
“np” orbital being filled
“(n – 1)d” orbital being filled
“( n – 2)f” orbital being filled
4
Li Be
n= 3 11 12
Na Mg
n= 4 19 20
21
B
C
N
O
F
10
Ne
13
14
15
16
17
Al
Si
P
S
Cl Ar
36
53
54
Rb Sr
Y
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
I
Xe
74
75
76
77
Cs Ba La Hf Ta W Re Os Ir
n= 7 87 88
78
79
80
81
82
51
35
52
73
50
34
40
72
49
33
39
57
48
32
n= 5 37 38
n= 6 55 56
47
31
18
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
46
30
9
V
45
29
8
K Ca Sc Ti
44
28
7
24
43
27
6
23
42
26
5
He
22
41
25
2
83
84
85
86
Pt Au Hg Tl Pb Bi Po At Rn
89 104 105 106 107 108 109 110 111
Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg
58
59
60
61
62
63
64
65
66
67
68
69
70
71
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
90
91
Th Pa
92
93
94
95
96
97
98
99 100 101 102 103
U Np Pu Am Cm Bk Cf Es Fm Md No Lr
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Chemistry: The Molecular Nature of Matter, 6E
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Read Periodic Table to Determine
Electron Configuration – He
 Read from left to
right
 First electron goes
into period 1
 First type of sublevel
to fill = “1s ”
 He has 2 two
electrons
 Electron
configuration for He
is: 1s 2
Jespersen/Brady/Hyslop
n= 1 1
2
“ns” orbital being filled He
“np” orbital being filled
“(n – 1)d” orbital being filled
“( n – 2)f” orbital being filled
H
n= 2 3
4
Li Be
n= 3 11
12
Na Mg
n= 4 19
22
23
24
K Ca Sc Ti
V
Cr Mn Fe Co Ni
n= 5 37
20
21
Rb Sr
Y
Zr Nb Mo Tc Ru Rh Pd
75
76
46
78
Cs Ba La Hf Ta W Re Os Ir
Pt
88
74
45
77
n= 7 87
73
44
28
40
72
43
27
39
57
42
26
38
n= 6 55 56
41
25
89 104 105 106 107 108 109 110
Fr Ra Ac Rf Db Sg Bh Hs Mt Ds
Chemistry: The Molecular Nature of Matter, 6E
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Electron Configuration of Boron (B)
n= 1 1
2
H
n= 2 3
4
Li Be
n= 3 11
12
Na Mg
n= 4 19
21
N
O
F
Ne
13
14
15
16
17
Al
Si
P
S
Cl Ar
36
54
Rb Sr
Y
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
I
Xe
74
75
76
77
Cs Ba La Hf Ta W Re Os Ir
n= 7 87 88
78
79
80
81
82
51
35
53
73
50
34
52
72
49
33
40
57
48
32
39
56
47
31
18
38
n= 6 55
46
30
C
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
45
29
B
10
V
44
28
9
K Ca Sc Ti
43
27
8
24
42
26
7
23
41
25
6
22
n= 5 37
20
5
He
83
84
85
86
Pt Au Hg Tl Pb Bi Po At Rn
89 104 105 106 107 108 109 110 111
Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg
 B has 5 electrons
 Fill first shell…
 Fill two subshells in second shell, in order of increasing
energy
22s 22p 1
 Electron Configuration
B
=
1
s
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Learning Check
Write the correct ground state electron configuration for
each of the following elements. List in order of
increasing n and within each shell, increasing ℓ.
1.
K
Z = 19
= 1 s 2 2s 2 2p 6 3s 2 3p 6 4s 1
2.
Ni
Z = 28
= 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 8
= 1 s 2 2s 2 2p 6 3s 2 3p 6 3 d 8 4s 2
3.
Pb
Z = 82
= 1s 2 2s 22p 63s 23p 64s 23d 104p 65s 24d 10 5p 66s 24f
145d 106p 2
= 1s 22s 22p 63s 23p 63d 104s 24p 64d 104f 145s 25p 65d 106s 26p 2
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Abbreviated Electron Configurations
- Noble Gas Notation
 [noble gas of previous row] and electrons filled
in next row
 Represents core + outer shell electrons
 Use to emphasize that only outer shell electrons
participate in chemical reactions
e.g.
Ba = [Xe] 6s 2
Ru = [Kr] 4d 6 5s 2
S = [Ne] 3s 2 3p 4
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Noble Gas Core Notation for Mn
 Find last noble gas that is filled before Mn
 Next fill sublevels that follow
[Ar] 4s 2 3d 5
n= 1 1
“ns” orbital being filled
“np” orbital being filled
“(n – 1)d” orbital being filled
“( n – 2)f” orbital being filled
H
n= 2 3
4
Li Be
n= 3 11 12
Na Mg
n= 4 19 20
21
22
23
n= 5 37 38
39
2
He
5
6
7
8
9
10
B
C
N
O
F Ne
13
14
15
16
S
17
18
Cl Ar
Al Si
P
V
24
25
26
27
28
29
30
31
32
33
34
35
36
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Y
40
41
42
43
44
45
46
47
48
49
50
51
52
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
53
54
n= 6 55 56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
n= 7 87 88
89 104 105 106 107 108 109 110 111
68
69
70
71
K Ca Sc Ti
Rb Sr
I Xe
Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg
58
59
60
61
62
63
64
65
66
67
90
91
92
93
94
95
96
97
98
99 100 101 102 103
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
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Your Turn!
The ground state electron configuration for Ca
is:
A. [Ar] 3s 1
B. 1s 2 2s 2 2p 6 3s 2 3p 5 4s 2
C. [Ar] 4s 2
D. [Kr] 4s 1
E. [Kr] 4s 2
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Look at Group 2A
Z Electron Configuration
4 1s 22s 2
Abbrev
Be
Mg 12 1s 22s 22p 63s 2
Ca 20 1s 22s 22p 63s 23p 64s 2
Sr 38 1s 22s 22p 63s 23p 63d 104s 24p 65s 2
[He] 2s 2
[Ne] 3s 2
[Ar] 4s 2
[Kr] 5s 2
Ba 56 1s 22s 22p 63s 23p 63d 104s 24p 64d 105s 25p 66s 2
[Xe] 6s 2
Ra 88 1s 22s 22p 63s 23p 63d 104s 24p 64d 104f 145s 25p 6 [Rn] 7s 2
5d 106s 26p 67s 2
 All have ns 2 outer shell electrons
 Only difference is value of n
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Your Turn!
An element with the electron configuration
[Xe]6s 24f 145d 7 would belong to which class on the
periodic table?
A. Transition elements
B. Alkaline earth elements
C. Halogens
D. Lanthanide elements
E. Alkali metals
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Shorthand Orbital Diagrams
 Write out lines for orbital beyond Noble gas
 Higher energy orbital to right
 Fill from left to right
Abbreviated Orbital Diagrams
Ru
[Kr]





4d
S
[Ne]
5s

 
3s
3p
Jespersen/Brady/Hyslop


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Your Turn!
Which of the following choices is the correct
electron configuration for a cobalt atom?
4s
3d
A. [Ar]
↑↓
↑↓ ↑↓ ↑↓ ↑
B. [Ar]
↑
↑↓ ↑↓ ↑↓ ↑↓
C. [Ar]
↑
↑↓ ↑↓ ↑↓ ↑
D. [Ar]
E. [Ar]
↑
↑↓ ↑↓ ↑↓ ↑↓ ↑
↑↓
Jespersen/Brady/Hyslop
↑↓ ↑↓ ↑
↑
↑
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Valence Shell Electron Configurations
 An even more abbreviated notation for electron
configurations
 Use with representative elements (s and p block
elements) – longer columns
 Electrons in s and p subshells - important for
bonding
 Valence shell = outer shell
= occupied shell with highest n
 Example:
Sn = 5s 25p 2
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Electronic Configurations
 A few exceptions to rules
Element
Cr
Cu
Ag
Au
Expected
[Ar] 3d 44s 2
[Ar] 3d 94s 2
[Kr] 4d 95s 2
[Xe] 5d 96s 2
Experimental
[Ar] 3d 54s 1
[Ar] 3d 104s 1
[Kr] 4d 105s 1
[Xe] 5d 106s 1
 Exactly filled and exactly half-filled subshells have
extra stability
 Promote one electron into ns orbital to gain this
extra stability
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Heisenberg’s Uncertainty Principle
 Can’t know both exact position and exact
speed of subatomic particle simultaneously
 Such measurements always have certain
minimum uncertainty associated with them
h
Dx Dmv ³
4p
x = particle position
mv = particle momentum
= mass × velocity of particle
h = Planck’s constant = 6.626 × 10–34 J s
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Consequence of Heisenberg’s
Uncertainty Principle
 Can’t talk about absolute position
 Can only talk about electron probabilities
 Where is e – likely to be?
 ψ = wavefunction
 Amplitude of electron wave
 ψ2 = probability of finding electron at given
location
 Probability of finding an electron in given region
of space equals the square of the amplitude of
wave at that point
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1s Orbital Representations
a. Dot-density diagram
b. Probability of finding electron around given point,
ψ2, with respect to distance from nucleus
c. Radial probability distribution = probability of
finding electron at an “r” distance from nucleus
 rmax = Bohr radius
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Electron Density Distribution
 Determined by

Shape
Size
n
Orientation m
 Electron density
 No sharp boundary
 Gradually fades away
 “Shape”
 Imaginary surface enclosing 90% of electron density
of orbital
 Probability of finding electrons is same everywhere on
surface
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Effect of n on s Orbital
 In any given direction
probability of finding
electron same
 All s orbitals are
spherically shaped
 Size increases as n
increases
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Spherical Nodes
 At higher n, now have spherical nodes
 Spherical regions of zero probability, inside orbital
 Node for electron wave
 Imaginary surface where electron density = 0
 2s, one spherical node, size larger
 3s, two spherical nodes, size larger yet
In general:
 Number of spherical nodes
=n–1
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p Orbitals
 Possess one nodal plane through nucleus
 Electron density only on two sides of nucleus
 Two lobes of electron density
 All p orbitals have same overall shape
 Size increases as n increases
 For 3p have one spherical node
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Representations of p Orbitals
 Constant probability surface for
2p orbital
 Simplified p orbital emphasizing
directional nature of orbital
 All 2p orbitals in p sub shell
 One points along each axis
2px
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2py
2pz
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There Are Five Different d Orbitals
 Four with four lobes of electron density
 One with two lobes and ring of electron density
 Result of two nodal planes though nucleus
 Number of nodal planes through nucleus = 
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Your Turn!
Which sketch represents a pz orbital?
A.
C.
B.
D.
E.
z
y
x
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Periodic Properties: Consequences of
Electron Configuration
 Chemical and physical properties of elements
 Vary systematically with position in periodic table
 i.e. with element's electron configuration
 To explain, must first consider amount of positive
charge felt by outer electrons (valence electrons)
 Core electrons spend most of their time closer to
nucleus than valence (outer shell) electrons
 Shield or cancel out (screen out, neutralize) some of
positive charge of nucleus
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Learning check: Li 1s 22s 1
 Three protons in
nucleus
 Two core electrons
in close (1s)
 Net positive charge
felt by outer electron:
 One proton
Effective Nuclear
Charge (Zeff)
 Net positive charge outer electron feels
 Core electrons shield valence electrons from full
nuclear charge
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Shielding
 Electrons in same subshell don't shield each other
 Same average distance from nucleus
 Trying to stay away from each other
 Spend very little time one below another
 Effective nuclear charge determined primarily by
 Difference between charge on nucleus (Z ) and charge
on core (number of inner electrons)
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Your Turn!
What value is the closest estimate of Zeff for a
valence electron of the calcium atom?
A. 1
B. 2
C. 6
D. 20
E. 40
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Atomic Size
 Experiment shows atoms/ions behave as if they
have definite size
 C and H have ~ same distance between nuclei in
large number of compounds
Atomic Radius (r)
 Half of distance between two like atoms
 H—H C—C etc.
 Usually use units of picometer
 1 pm = 1 × 10–12 m
 Range 37 – 270 pm for atoms
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Trends in Atomic Radius (r)
Increases down Column (group)
 Zeff essentially constant
 n increases, outer electrons farther away from
nucleus and radius increase
Decreases across row (period)
 n constant
 Zeff decreases, outer electrons feel larger Zeff and
radius decreases
Transition Metals and Inner Transition Metals
 Size variations less pronounced as filling core
 n same (outer electrons) across row
 Decrease in Zeff and r more gradually
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Atomic and Ionic Radii (in pm)
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Ionic Radii
 Increases down column
(group)
 Decreases across row (period)
Anions larger than parent atom
 Same Zeff, more electrons
 Radius expands
Cations smaller than parent atom
 Same Zeff, less electrons,
 Radius contracts
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Your Turn!
Which of the following has the smallest
radius?
A. Ar
B. K+
C. Cl–
D. Ca2+
E. S2–
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Ionization Energy
 Energy required to remove electron from gas
phase atom
 Corresponds to taking electron from n to n = 
 First ionization energy M (g)  M +(g) + e–
 IE = E
IE =
RHhcZ
n
2
eff
2
Trends:
 Ionization energy decreases down column (group)
as n increases
 Ionization energy increases across row (period) as
Zeff increases
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Comparing First Ionization Energies
 Largest first
ionization energies
are in upper right
 Smallest first
ionization energies
are in lower left
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Table 8.2: Successive Ionization Energies in
kJ/mol for H through Mg
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Electron Affinity (EA)
 Potential energy change associated with
addition of one electron to gas phase atom or
ion in the ground state
X(g) + e–  X –(g)
 O and F very favorable to add electrons
 First electron affinities usually negative
(exothermic)
 Larger negative value means more favorable to
add electron
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Table 8.3 Electron Affinities of Representative
Elements
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Trends in Electron Affinity (EA)
 Electron affinity becomes less exothermic down
column (group) as n increases
 Electron harder to add as orbital farther from nucleus
and feels less positive charge
 Electron affinity becomes more exothermic across
row (period) as Zeff increases
 Easier to attract electrons as positive charge
increases
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Successive Electron Affinities
 Addition of first electron – often exothermic
 Addition of more than one electron requires
energy
 Consider addition of electrons to oxygen:
Change:
EA(kJ/mol)
O(g) + e –  O–(g)
–141
O–(g) + e –  O2–(g)
+844
Net: O(g) + 2e –  O2–(g)
+703
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Your Turn!
Which of the following has the largest electron
affinity?
A. O
B. F
C. As
D. Cs
E. Ba
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