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Chemistry
Third Edition
Julia Burdge
Lecture PowerPoints
Chapter 6
Quantum Theory and
the Electronic Structure
of Atoms
Copyright © 2012, The McGraw-Hill Compaies, Inc. Permission required for reproduction or display.
CHAPTER
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6
Quantum Theory and the
Electronic Structure of Atoms
The Nature of Light
Quantum Theory
Bohr’s Theory of the Hydrogen Atom
Wave Properties of Matter
Quantum Mechanics
Quantum Numbers
Atomic Orbitals
Electron Configuration
Electron Configurations and the Periodic Table
2
6.1
The Nature of Light
Topics
Properties of Waves
The Electromagnetic Spectrum
The Double-Slit Experiment
3
6.1
The Nature of Light
Properties of Waves
When we say “light,” we generally mean visible light, which is
the light we can detect with our eyes.
Visible light, however, is only a small part of the continuum of
radiation that comprises the electromagnetic spectrum.
4
6.1
The Nature of Light
Properties of Waves
Wavelength  (lambda) is the distance between identical
points on successive waves (e.g., successive peaks or
successive troughs).
5
6.1
The Nature of Light
Properties of Waves
The frequency  (nu) is the number of waves that pass
through a particular point in 1 second.
6
6.1
The Nature of Light
Properties of Waves
Amplitude is the vertical distance from the midline of a wave
to the top of the peak or the bottom of the trough.
7
6.1
The Nature of Light
Properties of Waves
The speed of light through a vacuum, c, is
c = 2.99792458 × 108 m/s.
The speed, wavelength, and frequency of a wave are related
by the equation
where  and  are expressed in meters (m) and reciprocal
seconds (s–1), respectively.
8
SAMPLE PROBLEM
6.1
One type of laser used in the treatment of vascular skin
lesions is a neodymium-doped yttrium aluminum garnet or
Nd:YAG laser.
The wavelength commonly used in these treatments is 532
nm. What is the frequency of this radiation?
Setup
Solving for frequency gives  = c/.
9
SAMPLE PROBLEM
6.1
Solution
10
6.1
The Nature of Light
Properties of Waves
© Jim Wehtje/Getty Images
11
6.1
The Nature of Light
The Electromagnetic Spectrum
An electromagnetic wave
has an electric field
component and a
magnetic field
component.
These two components have
the same wavelength and frequency, and hence the same
speed, but they travel in mutually perpendicular planes.
12
6.1
The Nature of Light
The Double-Slit Experiment
13
6.2
Quantum Theory
Topics
Quantization of Energy
Photons and the Photoelectric Effect
14
6.2
Quantum Theory
Quantization of Energy
When a solid is heated, it emits electromagnetic radiation,
known as blackbody radiation, over a wide range of
wavelengths.
Attempts to model blackbody radiation in terms of
established wave theory and thermodynamic laws were only
partially successful.
Planck developed a successful model by proposing that
radiant energy could only be emitted or absorbed in discrete
quantities, like small packages or bundles.
15
6.2
Quantum Theory
Quantization of Energy
Planck gave the name quantum to the smallest quantity of
energy that can be emitted (or absorbed) in the form of
electromagnetic radiation.
The energy E of a single quantum of energy is given by
where h is called Planck’s constant and is the frequency of
the radiation.
The value of Planck’s constant is 6.63 × 10–34 J·s.
16
SAMPLE PROBLEM
6.2
How much more energy per photon is there in green light of
wavelength 532 nm than in red light of wavelength 635 nm?
Setup
17
SAMPLE PROBLEM
6.2
Solution
Following the same procedure, the energy of a photon of
wavelength 635 nm is 3.13 × 10–19 J.
18
SAMPLE PROBLEM
6.2
Solution
The difference between them is
(3.74 × 10–19 J) – (3.13 × 10–19 J) = 6.1 × 10–20 J.
Therefore, a photon of green light ( = 532 nm) has
6.1 × 10–20 J more energy than a photon of red light ( = 635
nm).
19
6.2
Quantum Theory
Photons and the Photoelectric Effect
In the photoelectric effect, electrons
are ejected from the surface of a
metal exposed to light of at least a
certain minimum frequency, called the
threshold frequency .
The photoelectric effect could not be
explained by the wave theory of light,
which associated the energy of light
with its intensity.
20
6.2
Quantum Theory
Photons and the Photoelectric Effect
Einstein, however, made an extraordinary assumption. He
suggested that a beam of light is really a stream of particles.
These particles of light are now called photons.
Using Planck’s quantum theory of radiation as a starting
point, Einstein deduced that each photon must possess
energy E given by the equation
where h is Planck’s constant and  is the frequency of the
light.
21
6.2
Quantum Theory
Photons and the Photoelectric Effect
If the frequency of the photons is such that h exactly equals
the energy that binds the electrons in the metal, then the
light will have just enough energy to knock the electrons
loose.
If we use light of a higher frequency, then not only will the
electrons be knocked loose, but they will also acquire some
kinetic energy. This situation is summarized by the equation
where KE is the kinetic energy of the ejected electron and W
is the binding energy of the electron in the metal.
22
SAMPLE PROBLEM
6.3
Calculate the energy (in joules) of
(a) a photon with a wavelength of 5.00 × 104 nm (infrared
region) and
(b) a photon with a wavelength of 52 nm (ultraviolet region).
(c) Calculate the kinetic energy of an electron ejected by the
photon in part (b) from a metal with a binding energy of
3.7 eV.
23
SAMPLE PROBLEM
6.3
Setup
(a)
(b)
(c)
24
SAMPLE PROBLEM
6.3
Solution
(b) Following the same procedure as in part (a), the energy of
a photon of wavelength 52 nm is 3.8 × 10–18 J.
25
6.3
Bohr’s Theory of the Hydrogen Atom
Topics
Atomic Line Spectra
The Line Spectrum of Hydrogen
26
6.3
Bohr’s Theory of the Hydrogen Atom
Atomic Line Spectra
The emission spectra of atoms in the gas phase do not show a
continuous spread of wavelengths from red to violet; rather,
the atoms produce bright lines in distinct parts of the visible
spectrum.
These line spectra are the emission of light only at specific
wavelengths.
27
6.3
Bohr’s Theory of the Hydrogen Atom
Atomic Line Spectra
28
6.3
Bohr’s Theory of the Hydrogen Atom
29
6.3
Bohr’s Theory of the Hydrogen Atom
Atomic Line Spectra
Johannes Rydberg developed an equation that could calculate
all the wavelengths of hydrogen’s spectral lines:
In this equation, now known as the Rydberg equation,  is the
wavelength of a line in the spectrum; R∞ is the Rydberg
constant (1.09737316 × 107 m–1); and n1 and n2 are positive
integers, where n2 > n1.
30
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
According to the laws of classical physics, an electron moving
in an orbit of a hydrogen atom would radiate away energy in
the form of electromagnetic waves.
Thus, such an electron would quickly spiral into the nucleus
and annihilate itself with the proton.
31
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
Bohr postulated that the electron in atomic hydrogen is
allowed to occupy only certain orbits of specific energies.
In other words, the energies of the electron are quantized.
An electron in any of the allowed orbits will not radiate
energy and therefore will not spiral into the nucleus.
32
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
Bohr showed that the energies that the electron in the
hydrogen atom can possess are given by
where n is an integer with values n = 1, 2, 3, and so on.
The most negative value, then, is reached when n = 1, which
corresponds to the most stable energy state. We call this the
ground state, the lowest energy state of an atom.
33
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
Each energy state in which n > 1 is called an excited state.
The radius of each circular orbit in Bohr’s model depends on
n2. Thus, as n increases from 1 to 2 to 3, the orbit radius
increases very rapidly.
Radiant energy absorbed by the atom causes the electron to
move from the ground state (n = 1) to an excited state (n > 1).
state.
34
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
Conversely, radiant energy (in the form of a photon) is
emitted when the electron moves from a higher-energy
excited state to a lower-energy excited state or the ground
state.
35
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
36
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
37
6.3
Bohr’s Theory of the Hydrogen Atom
The Line Spectrum of Hydrogen
38
6.3
Bohr’s Theory of the Hydrogen Atom
39
SAMPLE PROBLEM
6.4
Calculate the wavelength (in nm) of the photon emitted when
an electron transitions from the n = 4 state to the n = 2 state
in a hydrogen atom .
Setup
According to the problem, the transition is from n = 4 to n = 2,
so ni = 4 and nf = 2. The required constants are
h = 6.63 × 10–34 J · s and c = 3.00 × 108 m/s.
40
SAMPLE PROBLEM
6.4
Solution
41
6.4
Wave Properties of Matter
Topics
The de Broglie Hypothesis
Diffraction of Electrons
42
6.4
Wave Properties of Matter
The de Broglie Hypothesis
The waves generated by plucking a guitar string are standing
or stationary waves because they do not travel along the
string.
Some points on the string, called nodes, do not move at all;
that is, the amplitude of the wave at these points is zero.
There is a node at each end, and there may be one or more
nodes between the ends. The greater the frequency of
vibration, the shorter the wavelength of the standing wave
and the greater the number of nodes.
43
6.4
Wave Properties of Matter
The de Broglie Hypothesis
44
6.4
Wave Properties of Matter
The de Broglie Hypothesis
According to de Broglie, an electron in an
atom behaves like a standing wave.
However, only certain wavelengths are
possible or allowed.
The relationship between the
circumference of an allowed orbit (2r) and
the wavelength () of the electron is given
by
45
6.4
Wave Properties of Matter
The de Broglie Hypothesis
Because n is an integer, r can have only certain values (integral
multiples of ) as n increases from 1 to 2 to 3 and so on.
And, because the energy of the electron depends on the size
of the orbit (or the value of r), the energy can have only
certain values, too.
Thus, the energy of the electron in a hydrogen atom, if it
behaves like a standing wave, must be quantized.
46
6.4
Wave Properties of Matter
The de Broglie Hypothesis
De Broglie’s reasoning led to the conclusion that waves can
behave like particles and particles can exhibit wavelike
properties.
De Broglie deduced that the particle and wave properties are
related by the following expression:
where , m, and u are the wavelength associated with a
moving particle, its mass, and its velocity, respectively.
47
6.4
Wave Properties of Matter
The de Broglie Hypothesis
A wavelength calculated using
is usually referred to specifically as a de Broglie wavelength.
Likewise, we will refer to a mass calculated using the equation
as a de Broglie mass.
48
SAMPLE PROBLEM
6.5
Calculate the de Broglie wavelength of the “particle” in the
following two cases:
(a) a 25-g bullet traveling at 612 m/s, and
(b) an electron (m = 9.109 × 10–31 kg) moving at 63.0 m/s.
Setup
Planck’s constant, h, is 6.63 × 10–34 J · s or, for the purpose of
making the unit cancellation obvious, 6.63 × 10–34 kg · m2/s.
Remember that 1 J = 1 kg · m2/s2.
Solution
49
SAMPLE PROBLEM
6.5
Solution
50
6.4
Wave Properties of Matter
Diffraction of Electrons
Experiments demonstrate that electrons do indeed possess
wavelike properties.
By directing a beam of electrons
(which are most definitely
particles) through a thin piece of
gold foil, Thomson obtained a set
of concentric rings on a screen,
similar to the diffraction pattern
observed when X rays (which are
most definitely waves) were used.
Erwin Schrodinger, Wave Mechanical
Model of the Atom. 1926
51
6.5
Quantum Mechanics
Topics
The Uncertainty Principle
The Schrödinger Equation
The Quantum Mechanical Description of the Hydrogen
Atom
52
6.5
Quantum Mechanics
The Uncertainty Principle
To describe the problem of trying to locate a subatomic
particle that behaves like a wave, Werner Heisenberg
formulated what is now known as the Heisenberg uncertainty
principle:
It is impossible to know simultaneously both the momentum
p and the position x of a particle with certainty. Stated
mathematically,
53
6.5
Quantum Mechanics
The Uncertainty Principle
For a particle of mass m,
where x and u are the uncertainties in measuring the
position and velocity of the particle, respectively.
Thus, making measurement of the velocity of a particle more
precise means that the position must become
correspondingly less precise. Similarly, if the position of the
particle is known more precisely, its velocity measurement
must become less precise.
54
SAMPLE PROBLEM
6.6
An electron in a hydrogen atom is known to have a velocity of
5 × 106 m/s  1 percent.
Using the uncertainty principle, calculate the minimum
uncertainty in the position of the electron and, given that the
diameter of the hydrogen atom is less than 1 angstrom (Å),
comment on the magnitude of this uncertainty compared to
the size of the atom.
Setup
The mass of an electron is 9.11 × 10–31 kg. Planck’s constant,
h, is 6.63 × 10–34 kg · m2/s.
55
SAMPLE PROBLEM
6.6
Solution
The minimum uncertainty in the position x is 1 × 10–9 m = 10
Å.
The uncertainty in the electron’s position is 10 times larger
than the atom!
56
6.5
Quantum Mechanics
The Schrödinger Equation
Erwin Schrödinger, using a complex mathematical technique,
formulated an equation that describes the behavior and
energies of submicroscopic particles in general.
The Schrödinger equation requires advanced calculus to solve,
and we will not discuss it here.
The equation, however, incorporates both particle behavior,
in terms of mass m, and wave behavior, in terms of a wave
function  (psi), which depends on the location in space of
the system (such as an electron in an atom).
57
6.5
Quantum Mechanics
The Schrödinger Equation
The wave function itself has no direct physical meaning.
However, the probability of finding the electron in a certain
region in space is proportional to the square of the wave
function, 2.
The idea of relating 2 to probability stemmed from a wave
theory analogy.
58
6.5
Quantum Mechanics
The Quantum Mechanical Description of the Hydrogen Atom
The Schrödinger equation specifies the possible energy states
the electron can occupy in a hydrogen atom and identifies the
corresponding wave functions ().
These energy states and wave functions are characterized by
a set of quantum numbers (to be discussed shortly), with
which we can construct a comprehensive model of the
hydrogen atom.
59
6.5
Quantum Mechanics
The Quantum Mechanical Description of the Hydrogen Atom
The square of the wave
function, 2, defines the
distribution of electron density
in three-dimensional space
around the nucleus.
Regions of high electron density
represent a high probability of
locating the electron.
60
6.5
Quantum Mechanics
The Quantum Mechanical Description of the Hydrogen Atom
To distinguish the quantum mechanical description of an
atom from Bohr’s model, we speak of an atomic orbital,
rather than an orbit.
An atomic orbital can be thought of as the wave function of
an electron in an atom.
When we say that an electron is in a certain orbital, we mean
that the distribution of the electron density or the probability
of locating the electron in space is described by the square of
the wave function associated with that orbital.
61
6.5
Quantum Mechanics
The Quantum Mechanical Description of the Hydrogen Atom
An atomic orbital, therefore, has a characteristic energy, as
well as a characteristic distribution of electron density.
62
6.6
Quantum Numbers
Topics
Principal Quantum Number (n)
Angular Momentum Quantum Number (l)
Magnetic Quantum Number (ml)
Electron Spin Quantum Number (ms)
63
6.6
Quantum Numbers
Principal Quantum Number (n)
In quantum mechanics, three quantum numbers are required
to describe the distribution of electron density in an atom.
These numbers are derived from the mathematical solution
of Schrödinger’s equation for the hydrogen atom.
64
6.6
Quantum Numbers
Principal Quantum Number (n)
The principal quantum number (n) designates the size of the
orbital. The larger n is, the greater the average distance of an
electron in the orbital from the nucleus and therefore the
larger the orbital.
n = 1, 2, 3, …
65
6.6
Quantum Numbers
Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) describes the
shape of the atomic orbital.
The values of l are integers that depend on the value of the
principal quantum number, n.
For a given value of n, the possible values of l range from 0 to
n – 1.
66
6.6
Quantum Numbers
Angular Momentum Quantum Number (l)
A collection of orbitals with the same value of n is frequently
called a shell.
One or more orbitals with the same n and l values are
referred to as a subshell.
For example, the shell designated by n = 2 is composed of two
subshells: l = 0 and l = 1 (the allowed values of l for n = 2).
These subshells are called the 2s and 2p subshells where 2
denotes the value of n, and s and p denote the values of l.
67
6.6
Quantum Numbers
Magnetic Quantum Number (ml)
The magnetic quantum number (ml ) describes the
orientation of the orbital in space.
Within a subshell, the value of ml depends on the value of l.
For a certain value of l, there are (2l + 1) integral values of ml
as follows:
–l, …, 0 , …, +l
68
6.6
Quantum Numbers
69
6.6
Quantum Numbers
Magnetic Quantum Number (ml)
70
SAMPLE PROBLEM
6.7
What are the possible values for the magnetic quantum
number (ml) when the principal quantum number (n) is 3 and
the angular momentum quantum number (l) is 1?
Setup
The possible values of ml are –l, . . . , 0, . . . , +l.
Solution
The possible values of ml are –1, 0, and +1.
71
6.6
Quantum Numbers
Electron Spin Quantum Number (ms)
Whereas three quantum numbers are sufficient to describe
an atomic orbital, an additional
quantum number becomes
necessary to describe an electron
that occupies the orbital.
Electrons possess a magnetic field,
as if they were spinning.
72
6.6
Quantum Numbers
Electron Spin Quantum Number (ms)
To specify the electron’s spin, we use the electron spin
quantum number (ms).
Because there are two possible directions of spin, opposite
each other, ms has two possible values: +1/2 and –1/2.
Two electrons in the same orbital with opposite spins are
referred to as “paired.”
73
6.6
Quantum Numbers
Electron Spin Quantum Number (ms)
To summarize, we can designate an orbital in an atom with a
set of three quantum numbers.
These three quantum numbers indicate the size (n), shape (l),
and orientation (ml) of the orbital.
A fourth quantum number (ms) is necessary to designate the
spin of an electron in the orbital.
74
6.7
Atomic Orbitals
Topics
s Orbitals
p Orbitals
d Orbitals and Other Higher-Energy Orbitals
Energies of Orbitals
75
6.7
Atomic Orbitals
s Orbitals
For any value of the principal quantum number (n), the value
0 is possible for the angular momentum quantum number (l),
corresponding to an s subshell.
Furthermore, when l = 0, the magnetic quantum number (ml)
has only one possible value, 0, corresponding to an s orbital.
Therefore, there is an s subshell in every shell, and each s
subshell contains just one orbital, an s orbital.
76
6.7
Atomic Orbitals
77
6.7
Atomic Orbitals
s Orbitals
All s orbitals are spherical in shape but differ in size, which
increases as the principal quantum number increases.
78
6.7
Atomic Orbitals
p Orbitals
When the principal quantum number (n) is 2 or greater, the
value 1 is possible for the angular momentum quantum
number (l), corresponding to a p subshell.
And, when l = 1, the magnetic quantum number (ml) has
three possible values: –1, 0, and +1, each corresponding to a
different p orbital.
79
6.7
Atomic Orbitals
p Orbitals
Therefore, there is a p subshell in every shell for which n  2,
and each p subshell contains three p orbitals.
These three p orbitals are labeled px , py , and pz .
80
6.7
Atomic Orbitals
p Orbitals
These three p orbitals are identical in size, shape, and energy;
they differ from one another only in orientation.
Like s orbitals, p orbitals increase in size from 2p to 3p to 4p
orbital and so on.
81
6.7
Atomic Orbitals
d Orbitals and Other Higher-Energy Orbitals
When the principal quantum number (n) is 3 or greater, the
value 2 is possible for the angular momentum quantum
number (l), corresponding to a d subshell.
When l = 2, the magnetic quantum number (ml) has five
possible values, –2, –1, 0, +1, and +2, each corresponding to a
different d orbital.
82
6.7
Atomic Orbitals
d Orbitals and Other Higher-Energy Orbitals
83
6.7
Atomic Orbitals
d Orbitals and Other Higher-Energy Orbitals
All the 3d orbitals in an atom are identical in energy and are
labeled with subscripts denoting their orientation with
respect to the x, y, and z axes and to the planes defined by
them.
The d orbitals that have higher principal quantum numbers
(4d, 5d, etc.) have shapes similar to those shown for the 3d
orbitals .
84
6.7
Atomic Orbitals
d Orbitals and Other Higher-Energy Orbitals
The f orbitals are important when accounting for the
behavior of elements with atomic numbers greater than 57,
but their shapes are difficult to represent.
In general chemistry we will not concern ourselves with the
shapes of orbitals having l values greater than 2.
85
SAMPLE PROBLEM
6.8
List the values of n, l, and ml for each of the orbitals in a 4d
subshell.
Strategy
Consider the significance of the number and the letter in the
4d designation and determine the values of n and l.
There are multiple possible values for ml, which will have to
be deduced from the value of l.
86
SAMPLE PROBLEM
6.8
Setup
The integer at the beginning of an orbital designation is the
principal quantum number (n).
The letter in an orbital designation gives the value of the
angular momentum quantum number (l).
The magnetic quantum number (ml) can have integral values
of –l, . . . , 0, . . . , +l.
87
SAMPLE PROBLEM
6.8
Solution
The values of n and l are 4 and 2, respectively, so the possible
values of ml are –2, –1, 0, +1, and +2.
88
6.7
Atomic Orbitals
Energies of Orbitals
89
6.7
Atomic Orbitals
Energies of Orbitals
90
6.8
Electron Configuration
Topics
Energies of Atomic Orbitals in Many-Electron Systems
The Pauli Exclusion Principle
The Aufbau Principle
Hund’s Rule
General Rules for Writing Electron Configurations
91
6.8
Electron Configuration
Energies of Atomic Orbitals in Many-Electron Systems
The hydrogen atom is a particularly simple system because it
contains only one electron.
The electron may reside in the 1s orbital (the ground state),
or it may be found in some higher-energy orbital (an excited
state).
With many-electron systems, we need to know the groundstate electron configuration—that is, how the electrons are
distributed in the various atomic orbitals.
92
6.8
Electron Configuration
Energies of Atomic Orbitals in Many-Electron Systems
To do this, we need to know the relative energies of atomic
orbitals in a many-electron system, which differ from those in
a one-electron system such as hydrogen.
In many-electron atoms, electrostatic interactions cause the
energies of the orbitals in a shell to split.
93
6.8
Electron Configuration
94
6.8
Electron Configuration
The Pauli Exclusion Principle
According to the Pauli exclusion principle, no two electrons in
the same atom can have the same four quantum numbers.
If two electrons in an atom have the same n, l, and ml values
(meaning that they occupy the same orbital), then they must
have different values of ms; that is, one must have ms = –1/2
and the other must have ms = +1/2.
95
6.8
Electron Configuration
The Pauli Exclusion Principle
Because there are only two possible values for ms, and no two
electrons in the same orbital may have the same value for ms,
a maximum of two electrons may occupy an atomic orbital,
and these two electrons must have opposite spins.
Two electrons in the same orbital with opposite spins are said
to have paired spins.
96
6.8
Electron Configuration
The Pauli Exclusion Principle
Orbital Notation and Orbital Diagrams
97
6.8
Electron Configuration
The Aufbau Principle
We can continue the process of writing electron
configurations for elements based on the order of orbital
energies and the Pauli exclusion principle.
This process is based on the Aufbau principle, which makes it
possible to “build” the periodic table of the elements and
determine their electron configurations by steps.
Each step involves adding one proton to the nucleus and one
electron to the appropriate atomic orbital.
98
6.8
Electron Configuration
The Aufbau Principle
1s22s22p1
99
6.8
Electron Configuration
Hund’s Rule
According to Hund’s rule, the most stable arrangement of
electrons in orbitals of equal energy is the one in which the
number of electrons with the same spin is maximized.
100
6.8
Electron Configuration
Hund’s Rule
101
6.8
Electron Configuration
General Rules for Writing Electron Configurations
1. Electrons will reside in the available orbitals of the lowest
possible energy.
2. Each orbital can accommodate a maximum of two
electrons.
3. Electrons will not pair in degenerate orbitals if an empty
orbital is available.
4. Orbitals will fill in the order indicated in the following
figure.
102
6.8
Electron Configuration
103
SAMPLE PROBLEM
6.9
Write the electron configuration and give the orbital diagram
of a calcium (Ca) atom (Z = 20).
Strategy
Use the general rules given and the Aufbau principle to
“build” the electron confi guration of a calcium atom and
represent it with an orbital diagram.
Setup
Because Z = 20, we know that a Ca atom has 20 electrons.
104
SAMPLE PROBLEM
6.9
Solution
105
6.9
Electron Configurations and the Periodic
Table
Topics
Electron Configurations and the Periodic Table
106
6.9
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic Table
The electron configurations of all elements except hydrogen
and helium can be represented using a noble gas core, which
shows in brackets the electron configuration of the noble gas
element that most recently precedes the element in question,
followed by the electron configuration in the outermost
occupied subshells.
107
6.9
Electron Configurations and the Periodic
Table
108
6.9
Electron Configurations and the Periodic
Table
109
6.9
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic Table
Anomalies
110
6.9
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic Table
Anomalies
The reason for these anomalies is that a slightly greater
stability is associated with the half-filled (3d5) and completely
filled (3d10) subshells.
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6.9
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic Table
Anomalies
There are several other anomalies as well in the transition
metals, the lanthanides, and the actinides.
112
6.9
Electron Configurations and the Periodic
Table
Electron Configurations and the Periodic Table
113
SAMPLE PROBLEM
6.10
Write the electron configuration for an arsenic atom (Z = 33)
in the ground state.
Setup
The noble gas core for As is [Ar], where Z = 18 for Ar.
The order of filling beyond the noble gas core is 4s, 3d, and
4p.
Fifteen electrons must go into these subshells because there
are 33 – 18 = 15 electrons in As beyond its noble gas core.
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SAMPLE PROBLEM
6.10
Solution
115