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5.2 Electron Arrangement in Atoms >
Chapter 5
Electrons In Atoms
5.1 Revising the Atomic Model
5.2 Electron Arrangement
in Atoms
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
1
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5.2 Electron Arrangement in Atoms >
CHEMISTRY
& YOU
What makes the electron configuration
of an atom stable?
Energy and stability
play an important
role in determining
how electrons are
configured in an
atom.
2
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5.2 Electron Arrangement in Atoms > Electron Configurations
Electron Configurations
What are the three rules for
writing the electron
configurations of elements?
Three rules—the aufbau
principle, the Pauli exclusion
principle, and Hund’s rule—tell
you how to find the electron
configurations of atoms.
3
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5.2 Electron Arrangement in Atoms > Electron Configurations
The ways in which electrons are arranged
in various orbitals around the nuclei of
atoms are called electron configurations.
4
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5.2 Electron Arrangement in Atoms > Electron Configurations
Aufbau Principle
6p
5d
6s
4f
5p
4d
Increasing energy
5s
4p
4s
3p
3s
2p
2s
1s
5
3d
According to the aufbau principle,
electrons occupy the orbitals of lowest
energy first. In the aufbau diagram,
each box represents an atomic orbital.
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5.2 Electron Arrangement in Atoms > Electron Configurations
Aufbau Principle
6p
5d
6s
4f
5p
4d
Increasing energy
5s
4p
4s
3p
3s
2p
2s
1s
6
3d
The aufbau diagram shows the
relative energy levels of the various
atomic orbitals. Orbitals of greater
energy are higher on the diagram.
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5.2 Electron Arrangement in Atoms > Electron Configurations
Aufbau Principle
6p
5d
6s
4f
5p
4d
Increasing energy
5s
4p
4s
3p
3s
2p
2s
1s
7
3d
The range of energy levels within a
principal energy level can overlap
the energy levels of another
principal level.
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5.2 Electron Arrangement in Atoms > Electron Configurations
Pauli Exclusion Principle
• According to the Pauli exclusion principle,
an atomic orbital may describe at most two
electrons.
• To occupy the same orbital, two electrons
must have opposite spins; that is, the
electron spins must be paired.
8
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5.2 Electron Arrangement in Atoms > Electron Configurations
Pauli Exclusion Principle
• Spin is a quantum mechanical property of
electrons and may be thought of as
clockwise or counterclockwise.
• A vertical arrow indicates an electron and its
direction of spin ( or ).
• An orbital containing paired electrons is
written as .
9
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5.2 Electron Arrangement in Atoms > Electron Configurations
Hund’s Rule
According to Hund’s rule, electrons
occupy orbitals of the same energy in a
way that makes the number of electrons
with the same spin direction as large as
possible.
10
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5.2 Electron Arrangement in Atoms > Electron Configurations
Hund’s Rule
Three electrons would occupy three
orbitals of equal energy as follows.
Electrons then occupy each orbital
so that their spins are paired with the
first electron in the orbital.
11
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5.2 Electron Arrangement in Atoms > Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
• An oxygen
atom contains
eight
electrons.
12
Electron Configurations of Selected Elements
Element
1s
2s
2px 2py 2pz
3s
Electron
configuration
H
1s1
He
1s2
Li
1s22s1
C
1s22s22p2
N
1s22s22p3
O
1s22s22p4
F
1s22s22p5
Ne
1s22s22p6
Na
1s22s22p63s1
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5.2 Electron Arrangement in Atoms > Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
Electron Configurations of Selected Elements
• The 1s orbital
has two
electrons of
opposite spin.
13
Element
1s
2s
2px 2py 2pz
3s
Electron
configuration
H
1s1
He
1s2
Li
1s22s1
C
1s22s22p2
N
1s22s22p3
O
1s22s22p4
F
1s22s22p5
Ne
1s22s22p6
Na
1s22s22p63s1
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5.2 Electron Arrangement in Atoms > Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
Electron Configurations of Selected Elements
• The 1s orbital
has two
electrons of
opposite spin.
• The 2s orbital
also has two
electrons of
opposite spin.
14
Element
1s
2s
2px 2py 2pz
3s
Electron
configuration
H
1s1
He
1s2
Li
1s22s1
C
1s22s22p2
N
1s22s22p3
O
1s22s22p4
F
1s22s22p5
Ne
1s22s22p6
Na
1s22s22p63s1
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5.2 Electron Arrangement in Atoms > Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
• Each of the
three 2p orbitals
has one
electron. The
remaining
electron now
pairs with an
electron
occupying one
of the 2p
orbitals.
15
Electron Configurations of Selected Elements
Element
1s
2s
2px 2py 2pz
3s
Electron
configuration
H
1s1
He
1s2
Li
1s22s1
C
1s22s22p2
N
1s22s22p3
O
1s22s22p4
F
1s22s22p5
Ne
1s22s22p6
Na
1s22s22p63s1
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5.2 Electron Arrangement in Atoms > Electron Configurations
• A convenient shorthand method for showing
the electron configuration of an atom involves
writing the energy level and the symbol for
every sublevel occupied by an electron.
• You indicate the number of electrons
occupying that sublevel with a superscript.
16
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5.2 Electron Arrangement in Atoms > Electron Configurations
• For hydrogen, with one electron in a 1s
orbital, the electron configuration is
written 1s1.
• For oxygen, with two electrons in a 1s
orbital, two electrons in a 2s orbital, and
four electrons in 2p orbitals, the electron
configuration is 1s22s22p4.
Note that the sum of the superscripts
equals the number of electrons in the
atom.
17
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5.2 Electron Arrangement in Atoms >
CHEMISTRY
& YOU
Explain why the correct electron
configuration of oxygen is
1s22s22p4 and not 1s22s22p33s1.
18
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5.2 Electron Arrangement in Atoms >
Sample Problem 5.1
Writing Electron Configurations
The atomic number of phosphorus is 15.
Write the electron configuration of a
phosphorus atom.
19
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5.2 Electron Arrangement in Atoms > Electron Configurations
Exceptional Electron Configurations
• You can obtain correct electron configurations
for the elements up to vanadium (atomic
number 23) by following the aufbau diagram for
orbital filling.
• If you were to continue in that fashion, however,
you would assign chromium and copper the
following incorrect configurations.
Cr 1s22s22p63s23p63d44s2
Cu 1s22s22p63s23p63d94s2
20
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5.2 Electron Arrangement in Atoms > Electron Configurations
Exceptional Electron Configurations
• The correct electron configurations are as
follows:
Cr 1s22s22p63s23p63d54s1
Cu 1s22s22p63s23p63d104s1
• These arrangements give chromium a
half-filled d sublevel and copper a filled d
sublevel.
21
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5.2 Electron Arrangement in Atoms > Electron Configurations
Exceptional Electron Configurations
Some actual electron configurations
differ from those assigned using the
aufbau principle because although
half-filled sublevels are not as stable
as filled sublevels, they are more
stable than other configurations.
22
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5.2 Electron Arrangement in Atoms >
What is the correct electron
configuration of a sulfur atom?
A. 1s22s22p43s23p6
B. 1s22s22p63s23p3
C. 1s22s22p63s23p4
D. 1s22s22p63s63p2
23
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5.2 Electron Arrangement in Atoms > Key Concept
Three rules—the aufbau principle, the Pauli
exclusion principle, and Hund’s rule—tell you
how to find the electron configurations of
atoms.
24
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5.2 Electron Arrangement in Atoms > Glossary Terms
• electron configuration: the arrangement of
electrons of an atom in its ground state into various
orbitals around the nuclei of atoms
• aufbau principle: the rule that electrons occupy the
orbitals of lowest energy first
• Pauli exclusion principle: an atomic orbital may
describe at most two electrons, each with opposite
spin direction
• spin: a quantum mechanical property of electrons; it
may be thought of as clockwise or counterclockwise
• Hund’s rule: electrons occupy orbitals of the same
energy in a way that makes the number of electrons
with the same spin direction as large as possible
25
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5.2 Electron Arrangement in Atoms >
Chapter 5
Electrons In Atoms
5.1 Revising the Atomic Model
5.2 Electron Arrangement in Atoms
5.3 Atomic Emission Spectra
and the Quantum
Mechanical Model
26
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5.2 Electron Arrangement in Atoms >
CHEMISTRY
& YOU
What gives gas-filled lights their colors?
An electric current
passing through the gas
in each glass tube
makes the gas glow
with its own
characteristic color.
27
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
Light and Atomic Emission Spectra
What causes atomic emission
spectra?
28
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The Nature of Light
• By the year 1900, there was
enough experimental evidence to
convince scientists that light
consisted of waves.
• The amplitude of a wave is the
wave’s height from zero to the
crest.
• The wavelength, represented by
 (the Greek letter lambda), is the
distance between the crests.
29
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The Nature of Light
• The frequency, represented by  (the
Greek letter nu), is the number of wave
cycles to pass a given point per unit of
time.
• The SI unit of cycles per second is called
the hertz (Hz).
30
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The Nature of Light
The product of frequency and wavelength
equals a constant (c), the speed of light.
c = 
31
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The frequency () and wavelength () of
light are inversely proportional to each
other. As the wavelength increases, the
frequency decreases.
32
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The Nature of Light
According to the wave model, light consists of
electromagnetic waves.
• Electromagnetic radiation includes
radio waves, microwaves, infrared
waves, visible light, ultraviolet waves,
X-rays, and gamma rays.
• All electromagnetic waves travel in a
vacuum at a speed of 2.998  108 m/s.
33
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The Nature of Light
The sun and incandescent light bulbs emit white
light, which consists of light with a continuous
range of wavelengths and frequencies.
• When sunlight passes through a prism, the
different wavelengths separate into a
spectrum of colors.
• In the visible spectrum, red light has the
longest wavelength and the lowest
frequency.
34
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
The electromagnetic spectrum consists of
radiation over a broad range of wavelengths.
Low energy
( = 700 nm)
Frequency  (s-1)
3 x 106
102
Wavelength  (m)
35
High energy
( = 380 nm)
3 x 1012
3 x 1022
10-8
10-14
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
Atomic Emission Spectra
When atoms absorb energy, their
electrons move to higher energy
levels. These electrons lose energy by
emitting light when they return to
lower energy levels.
36
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
Atomic Emission Spectra
A prism separates light into the colors it
contains. White light produces a rainbow
of colors.
Screen
Light
bulb
37
Slit
Prism
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
Atomic Emission Spectra
Light from a helium lamp produces
discrete lines.
Screen
38
Helium
lamp
Slit
Prism
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5.2 Electron Arrangement in Atoms >Light and Atomic
Emission Spectra
Atomic Emission Spectra
• The energy absorbed by an electron for it to move
from its current energy level to a higher energy level
is identical to the energy of the light emitted by the
electron as it drops back to its original energy level.
• The wavelengths of the spectral lines are
characteristic of the element, and they make up the
atomic emission spectrum of the element.
• No two elements have the same emission spectrum.
39
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
Calculating the Wavelength of Light
Calculate the wavelength of the
yellow light emitted by a
sodium lamp if the frequency of
the radiation is 5.09 × 1014 Hz
(5.09 × 1014/s).
40
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
1 Analyze List the knowns and the unknown.
Use the equation c =  to solve for the
unknown wavelength.
KNOWNS
frequency () = 5.09 × 1014 /s
c = 2.998 × 108 m/s
UNKNOWN
wavelength () = ? m
41
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
2 Calculate Solve for the unknown.
Write the expression that relates the
frequency and wavelength of light.
c = 
42
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
2 Calculate Solve for the unknown.
Rearrange the equation to solve for .
c = 
c
= 
43
Solve for  by
dividing both sides

by :c
 = 
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
2 Calculate Solve for the unknown.
Substitute the known values for  and c into
the equation and solve.
c
2.998  108 m/s
–7 m
=
=
=
5.89

10

5.09  1014 /s
44
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5.2 Electron Arrangement in Atoms > Sample Problem 5.2
3 Evaluate Does the answer make sense?
The magnitude of the frequency is much
larger than the numerical value of the
speed of light, so the answer should be
much less than 1. The answer should have
3 significant figures.
45
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Quantum Concept and Photons
How did Einstein explain the
photoelectric effect?
46
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Quantization of Energy
German physicist Max Planck (1858–1947)
showed mathematically that the amount of
radiant energy (E) of a single quantum
absorbed or emitted by a body is proportional
to the frequency of radiation ().
E
47
 or E = h
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Quantization of Energy
The constant (h), which has a value of 6.626
 10–34 J·s (J is the joule, the SI unit of
energy), is called Planck’s constant.
E
48
 or E = h
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
Albert Einstein used Planck’s quantum theory
to explain the photoelectric effect.
In the photoelectric effect, electrons
are ejected when light shines on a
metal.
49
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
Not just any frequency of light will cause the
photoelectric effect.
• Red light will not cause potassium to eject
electrons, no matter how intense the light.
• Yet a very weak yellow light shining on
potassium begins the effect.
50
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
• The photoelectric effect could not be
explained by classical physics.
• Classical physics correctly described light as
a form of energy.
• But, it assumed that under weak light of any
wavelength, an electron in a metal should
eventually collect enough energy to be
ejected.
51
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
To explain the photoelectric effect,
Einstein proposed that light could be
described as quanta of energy that
behave as if they were particles.
52
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
These light quanta are called photons.
• Einstein’s theory that light behaves as a stream
of particles explains the photoelectric effect
and many other observations.
• Light behaves as waves in other situations; we
must consider that light possesses both
wavelike and particle-like properties.
53
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5.2 Electron Arrangement in Atoms > The Quantum Concept
and Photons
The Photoelectric Effect
No electrons are ejected
because the frequency
of the light is below the
threshold frequency.
54
If the light is at or above
the threshold frequency,
electrons are ejected.
If the frequency is
increased, the ejected
electrons will travel
faster.
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5.2 Electron Arrangement in Atoms > Sample Problem 5.3
Calculating the Energy of a Photon
What is the energy of
a photon of
microwave radiation
with a frequency of
3.20 × 1011/s?
55
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5.2 Electron Arrangement in Atoms > Sample Problem 5.3
1 Analyze List the knowns and the unknown.
Use the equation E = h ×  to calculate the
energy of the photon.
KNOWNS
frequency () = 3.20 × 1011/s
h = 6.626 × 10–34 J·s
UNKNOWN
energy (E) = ? J
56
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5.2 Electron Arrangement in Atoms > Sample Problem 5.3
2 Calculate Solve for the unknown.
Write the expression that relates the
energy of a photon of radiation and the
frequency of the radiation.
E = h
57
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5.2 Electron Arrangement in Atoms > Sample Problem 5.3
2 Calculate Solve for the unknown.
Substitute the known values for  and h
into the equation and solve.
E = h = (6.626  10–34 J·s)  (3.20  1011/s)
= 2.12  10–22 J
58
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5.2 Electron Arrangement in Atoms > Sample Problem 5.3
3 Evaluate Does the result make sense?
Individual photons have very small
energies, so the answer seems
reasonable.
59
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5.2 Electron Arrangement in Atoms >
What is the frequency of a photon
whose energy is 1.166  10–17 J?
E = h
E
=
h
E 6.626  10–34 J
 = h = 1.166  10–17 J·s = 1.760  1016 Hz
60
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5.2 Electron Arrangement in Atoms >An Explanation of
Atomic Spectra
An Explanation of Atomic Spectra
How are the frequencies of light
emitted by an atom related to
changes of electron energies?
61
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5.2 Electron Arrangement in Atoms >An Explanation of
Atomic Spectra
When an electron has its lowest possible
energy, the atom is in its ground state.
• In the ground state, the principal quantum
number (n) is 1.
• Excitation of the electron by absorbing
energy raises the atom to an excited state
with n = 2, 3, 4, 5, or 6, and so forth.
• A quantum of energy in the form of light is
emitted when the electron drops back to a
lower energy level.
62
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5.2 Electron Arrangement in Atoms >An Explanation of
Atomic Spectra
The light emitted by an electron
moving from a higher to a lower
energy level has a frequency
directly proportional to the energy
change of the electron.
63
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5.2 Electron Arrangement in Atoms >An Explanation of
Atomic Spectra
The three groups of lines in the hydrogen
spectrum correspond to the transition of
electrons from higher energy levels to lower
energy levels.
64
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5.2 Electron Arrangement in Atoms >
CHEMISTRY
& YOU
The glass tubes in lighted signs contain helium,
neon, argon, krypton, or xenon gas, or a mixture
of these gases. Why do the colors of the light
depend on the gases that are used?
Each different gas has
its own characteristic
emission spectrum,
creating different colors
of light when excited
electrons return to the
ground state.
65
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5.2 Electron Arrangement in Atoms >
In the hydrogen spectrum, which of
the following transitions produces a
spectral line of the greatest energy?
A. n = 2 to n = 1
B. n = 3 to n = 2
C. n = 4 to n = 3
66
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
Quantum Mechanics
How does quantum mechanics
differ from classical mechanics?
67
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
Given that light behaves as waves and
particles, can particles of matter behave as
waves?
• Louis de Broglie referred to the wavelike
behavior of particles as matter waves.
• His reasoning led him to a mathematical
expression for the wavelength of a moving
particle.
68
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
The Wavelike Nature of Matter
Today, the wavelike properties of beams of
electrons are useful in viewing objects that cannot
be viewed with an optical microscope.
• The electrons in an electron
microscope have much smaller
wavelengths than visible light.
• These smaller wavelengths allow a
much clearer enlarged image of a
very small object, such as this pollen
grain, than is possible with an ordinary
microscope.
69
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
Classical mechanics adequately
describes the motions of bodies
much larger than atoms, while
quantum mechanics describes the
motions of subatomic particles
and atoms as waves.
70
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle
states that it is impossible to know both the
velocity and the position of a particle at the
same time.
71
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle
states that it is impossible to know both the
velocity and the position of a particle at the
same time.
• This limitation is critical when dealing with
small particles such as electrons.
• But it does not matter for ordinary-sized
objects such as cars or airplanes.
72
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5.2 Electron Arrangement in Atoms > Quantum Mechanics
• To locate an electron, you might strike it with a photon.
• The electron has such a small mass that striking it with a
photon affects its motion in a way that cannot be
predicted accurately.
• The very act of measuring the position of the electron
changes its velocity, making its velocity uncertain.
Before collision:
A photon strikes
an electron
during an attempt
to observe the
electron’s
position.
73
After collision:
The impact
changes the
electron’s velocity,
making it
uncertain.
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5.2 Electron Arrangement in Atoms >
The Heisenberg uncertainty principle
states that it is impossible to
simultaneously know which two
attributes of a particle?
velocity and position
74
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5.2 Electron Arrangement in Atoms > Key Concepts and
Key Equations
When atoms absorb energy, their electrons move
to higher energy levels. These electrons lose
energy by emitting light when they return to lower
energy levels.
To explain the photoelectric effect, Einstein
proposed that light could be described as quanta
of energy that behave as if they were particles.
The light emitted by an electron moving from a
higher to a lower energy level has a frequency
directly proportional to the energy change of the
electron.
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5.2 Electron Arrangement in Atoms > Key Concepts and
Key Equations
Classical mechanics adequately describes
the motions of bodies much larger than
atoms, while quantum mechanics describes
the motions of subatomic particles and atoms
as waves.
C = 
E=h
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5.2 Electron Arrangement in Atoms > Glossary Terms
• amplitude: the height of a wave’s crest
• wavelength: the distance between adjacent
crests of a wave
• frequency: the number of wave cycles that
pass a given point per unit of time; frequency
and wavelength are inversely proportional to
each other
• hertz: the unit of frequency, equal to one
cycle per second
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5.2 Electron Arrangement in Atoms > Glossary Terms
• electromagnetic radiation: energy waves
that travel in a vacuum at a speed of 2.998 
108 m/s; includes radio waves, microwaves,
infrared waves, visible light, ultraviolet
waves, X-rays, and gamma rays
• spectrum: wavelengths of visible light that
are separated when a beam of light passes
through a prism; range of wavelengths of
electromagnetic radiation
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5.2 Electron Arrangement in Atoms > Glossary Terms
• atomic emission spectrum: the pattern
formed when light passes through a prism or
diffraction grating to separate it into the
different frequencies of light it contains
• Planck’s constant: the constant (h) by
which the amount of radiant energy (E) is
proportional to the frequency of the radiation
()
• photoelectric effect: the phenomenon in
which electrons are ejected when light
shines on a metal
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5.2 Electron Arrangement in Atoms > Glossary Terms
• photon: a quantum of light; a discrete
bundle of electromagnetic energy that
interacts with matter similarly to particles
• ground state: the lowest possible energy of
an atom described by quantum mechanics
• Heisenberg uncertainty principle: it is
impossible to know both the velocity and the
position of a particle at the same time
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5.2 Electron Arrangement in Atoms > BIG IDEA
Electrons and the Structure of Atoms
• Electrons can absorb energy to move from
one energy level to a higher energy level.
• When an electron moves from a higher
energy level back down to a lower energy
level, light is emitted.
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