1. science
2. physics

Objectives
• Describe the two primary
models of light. (38.1)
38
• Explain how the energy of
a photon is related to its
frequency. (38.2)
• Describe what the photoelectric
effect suggests about the way
light interacts with matter.
(38.3)
• Explain what causes light to
behave like a wave and what
causes light to behave like a
particle. (38.4)
• Describe what de Broglie
suggested about all matter.
(38.5)
• Describe electron orbits
according to de Broglie’s
theory of matter waves. (38.6)
• Explain what determines the
radii of the electron orbits in
the Bohr model of the atom.
(38.7)
THE ATOM
AND THE QUANTUM
..........
THE ATOM
AND THE
QUANTUM
THE BIG
IDEA
Material particles and light
have both wave properties and
particle properties.
T
he final unit of this book is about
the realm of the unimaginably tiny
atom. This chapter investigates
atomic structure, which is revealed
by analyzing light. Light has a dual
nature, which in turn radically alters
our understanding of the atomic
world. The next chapter covers
the structure of the atomic nucleus
and radioactivity, and the concluding chapter is about the nuclear
processes of fission and fusion.
• Describe the laws governing
subatomic interactions. (38.8)
• Explain what determines
predictability in orderly
systems. (38.9)
This chapter can, with
some discussion of atomic
spectra, stand on its own as a
continuation and conclusion of
Chapter 17, The Atomic Nature
of Matter. For a short course,
Chapter 10 followed by this
chapter should work quite
well. It is background for
Chapters 39 and 40, but is not
a prerequisite.
766
discover!
How Can Waves Behave as Particles and
Particles Behave as Waves?
1. Draw a square with sides of approximately
5 cm.
2. Draw a second square of the same size on
top, but slightly displaced to the side, of the
first square.
3. Form a cube by connecting the two squares
with straight lines connected to the corresponding vertices.
4. Stare at the cube until you observe a change
in the drawing.
766
Analyze and Conclude
1. Observing Describe any changes you
observed in the appearance of the cube.
2. Predicting Do you think you would
observe similar changes when viewing other
figures or objects?
3. Making Generalizations Suggest other situations in which there are two equally valid
points of view.
discover!
MATERIALS
FIGURE 38.1
EXPECTED OUTCOME Students
will observe that they can see
two different aspects of the
cube, but not simultaneously.
In the old planetary
model of the atom,
the electrons orbit the
nucleus like little planets
around a tiny sun.
ANALYZE AND CONCLUDE
1. After some time you
observe two different
aspects of the cube.
38.1 Models
......
CHECK
2. Yes, when the brain is
presented with sensory
information from a figure
that may be decoded in two
equally satisfactory ways.
3. Under certain circumstances,
light behaves as if it were
a wave, but under other
conditions it exhibits
particle-like properties.
38.1 Models
Teaching Tip Don’t overdo
history here if physics is your
game. The history is more
interesting to those already
familiar with physics.
Through the
centuries there have
been two primary models of
light: the particle model and the
wave model.
......
Nobody knows what an atom’s internal structure looks like, for there
is no way to see it with our eyes. To visualize the processes that occur
in the subatomic realm, we construct models. Figure 38.1 shows the
planetary model—the one that most people think of when they picture an atom—in which the electrons orbit the nucleus like planets
going around the sun. This was an early model of the atom suggested
by the Danish physicist Niels Bohr in 1913. We still tend to think in
terms of this simple picture, even though it has been replaced by a
more complex model in which the electrons are represented as clouds
spread throughout the interior of the atom, as shown in Figure 38.2.
We will see that the planetary model of the atom is still useful for
understanding the emission of light.
Models are assessed not in terms of their “truthfulness,” but in
terms of their “usefulness.” Models help us to understand processes
that are difficult to visualize. A useful model of the atom must be consistent with a model for light, for most of what we know about atoms
we learn from the light and other radiations they emit. Most light has
its source in the motion of electrons within the atom.
Through the centuries there have been two primary models of
light: the particle model and the wave model. Isaac Newton believed
light was composed of a hail of tiny particles. Christian Huygens
believed that light was a wave phenomenon. The wave model was reinforced more than a century later when Thomas Young demonstrated
that light exhibited constructive and destructive interference. Later,
James Clerk Maxwell proposed that light is an electromagnetic wave
and a part of a broader electromagnetic spectrum. The wave model
gained further support when Heinrich Hertz produced radio waves
that behaved as Maxwell had predicted. This seemed to verify the wave
nature of light once and for all. But Maxwell’s electromagnetic wave
model was not the last word on the nature of light. In 1905 Albert
Einstein resurrected the particle theory of light.
CONCEPT
pencil or pen,
paper
CONCEPT
CHECK
FIGURE 38.2 In the current model of
the atom, electrons are
spread out in waves or
clouds.
Teaching Resources
• Reading and Study
Workbook
• PresentationEXPRESS
• Interactive Textbook
• Next-Time Question 38-1
• Conceptual Physics Alive!
DVDs Atoms
What are the two primary models of light?
CHAPTER 38
THE ATOM AND THE QUANTUM
767
767
38.2 Light Quanta
38.2 Light Quanta
Key Terms
quantum (pl. quanta), photon,
Planck’s constant
Teaching Tip Recall that
different colors of light have
different frequencies—red lowest
and violet highest. Below red
is the infrared (IR) part of the
electromagnetic spectrum, and
above violet, the ultraviolet
(UV). State that these different
frequencies have corresponding
energies—red lowest and violet
highest. Summarize this by
writing the proportion E ~ f and
state that the energy of a packet
of light energy, a photon, is
directly proportional to
its frequency.
For: Links on Max Planck
Visit: www.SciLinks.org
Web Code: csn – 3802
Ask Why do photographers
use red light in their darkrooms?
The low-energy photons in
red light do not affect
photographic film.
Teaching Tip State that the
ratio of the energy of light E
to its frequency f is always the
same: 6.67 3 10]34 J?s, or Planck’s
constant, abbreviated h. The
proportion is expressed as an
exact equation, E 5 hf.
......
The energy of a
photon is directly
proportional to the photon’s
frequency.
CONCEPT
......
CONCEPT How is the energy of a photon related to its
CHECK
Teaching Resources
• Reading and Study
Workbook
• Problem-Solving Exercises
in Physics 19-1
CHECK
frequency?
FIGURE 38.3 The energy of a photon
of light is proportional to
its vibrational frequency.
RED PHOTON
LONG WAVELENGTH
LOW FREQUENCY
• PresentationEXPRESS
• Interactive Textbook
768
Einstein visualized particles of light as concentrated bundles of electromagnetic energy. Einstein built on the idea of a German physicist,
Max Planck, who a few years earlier had proposed that atoms do not
emit and absorb light continuously, but do so in little chunks. Each
chunk was considered a quantum, or a fundamental unit. (The
plural of quantum is quanta.) Planck believed that light existed as
continuous waves, just as Maxwell had asserted, but that emission
and absorption occurred in quantum chunks. Einstein went further
and proposed that light itself is composed of quanta. One quantum
of light energy is now called a photon.
The idea that certain quantities are quantized—that they come
in discrete (separate) units—was known in Einstein’s time. Matter
is quantized. The mass of a gold ring, for example, is equal to some
whole-number multiple of the mass of a single gold atom. Electric
charge is quantized, as all charge is some whole-number multiple of
the charge of a single electron.
Other quantities such as energy and angular momentum are
quantized. The energy in a light beam is quantized and comes in packets, or quanta; only a whole number of quanta can exist. The quanta
of light, or of electromagnetic radiation in general, are the photons.
Photons have no rest energy. They move at one speed only—at
the speed of light! The total energy of a photon is the same as its
kinetic energy. The energy of a photon is directly proportional
to the photon’s frequency. This relationship is illustrated in Figure
38.3. When the energy E of a photon is divided by its frequency f, the
quantity that results is known as Planck’s constant, h. This quantity
is always the same, no matter what the frequency. The energy of every
photon is therefore E = hf.
This equation gives the smallest amount of energy that can be
converted to light of frequency f. Light is not emitted continuously,
but as a stream of photons, each with an energy hf.
768
BLUE PHOTON—
SHORT WAVELENGTH
HIGH FREQUENCY
38.3 The
38.3 The Photoelectric Effect
Photoelectric Effect
Einstein found support for his quantum theory of light in the photoelectric effect. The photoelectric effect is the ejection of electrons
from certain metals when light falls upon them. These metals are
said to be photosensitive (that is, sensitive to light). This effect is used
in electric eyes, in the photographer’s light meter, and in picking up
sound from the soundtracks of motion pictures.
Key Term
photoelectric effect
Demonstration
FIGURE 38.4
The photoelectric effect depends
on the frequency of light that
shines on the metal.
Explanation of the Photoelectric Effect The photoelectric
effect is illustrated in Figure 38.4. Energy from the light shining on
the metal plate gives electrons bound in the metal enough energy to
escape. Investigators discovered that high-frequency light, even from
a dim source, was capable of ejecting electrons from a photosensitive
metal surface; yet low-frequency light, even from a very bright source,
could not dislodge electrons. Since bright light carries more energy
than dim light, it was puzzling that dim blue or violet light could dislodge electrons from certain metals when bright red light could not.
Einstein explained the photoelectric effect by thinking of light
in terms of photons. The absorption of a photon by an atom in
the metal surface is an all-or-nothing process. Only one photon is
absorbed by each electron ejected from the metal. The number of
photons that hit the metal has nothing to do with whether a given
electron will be ejected. If the energy in the photon is large enough,
the electron will be ejected from the metal. But if the energy in the
photon is too small, then the electron is not ejected. The intensity of
light does not matter. From E = hf, the critical factor is the frequency,
or color, of the light. Since each blue or violet light photon carries
enough energy to free an electron from the metal, a few photons of
blue or violet light can eject a few electrons. But hordes of red or
orange photons cannot eject a single electron. Only high-frequency
photons have the energy needed to pull loose an electron.
Support for the Particle Model of Light The energy of a
wave is spread out along a broad front. For the energy of a light wave
to be concentrated enough to eject a single electron from a metal surface is as unlikely as for an ocean wave to hurl a boulder off the beach
with an energy equal to the energy of the whole wave.
CHAPTER 38
think!
Will high-frequency light
eject a greater number of
electrons than lowfrequency light?
Answer: 38.3
Light travels as a wave
and hits as a particle.
THE ATOM AND THE QUANTUM
769
Show a simulated
photoelectric effect with a
tennis ball in a small shallow
box. The tennis ball represents
an electron. Toss a lightweight
foam ball (painted red) at the
tennis ball to show that it does
not have enough energy to
knock the tennis ball out of
the box. Then toss a heavier
ball (painted blue) into the
box and out the tennis ball
pops. The red ball represents
a photon of red light—a small
KE. The blue ball represents
a photon of blue or violet
light—a greater KE. Explain
that high-energy photons
knock electrons from the
material whereas low-energy
photons don’t. Simulate the
work function of the material
by adjusting the depth of the
box with slabs of material
that cover its bottom. A deepset ball is more difficult to
dislodge than one resting on
a slab that is nearly as thick as
the box is deep.
There is a lot of confusion in
the minds of many people about
the wave-particle duality—more
than is warranted. It so happens
that light behaves like waves
when it travels in empty space,
and like particles when it
interacts with solid matter. It
is a mistake to insist it must be
both a particle and a wave at
the same time. What something
is and what it does are not the
same.
769
Demonstration
The photoelectric effect suggests that light interacts with
matter as a stream of particle-like photons. The number of photons
in a light beam controls the brightness of the whole beam, but the
frequency of the light controls the energy of each individual photon.
Experimental verification of Einstein’s explanation of the photoelectric effect was made 11 years later by the American physicist
Robert Millikan. Every aspect of Einstein’s interpretation was confirmed, including the direct proportionality of photon energy to
frequency. It was for this (and not for his theory of relativity) that
Einstein received the Nobel Prize.
......
Light quanta, electrons,
and other particles all
behave in some ways as
if they were lumps and
in other ways as if they
were waves.
CONCEPT
CHECK
What does the photoelectric effect suggest about
the way light interacts with matter?
38.4 Waves as Particles
FIGURE 38.5 Stages of the exposure of
film to light reveal the photon-by-photon production of
a photograph. The approximate numbers of photons at
each stage were a. 3 ⫻ 103,
b. 1.2 ⫻ 104, c. 9.3 ⫻ 104,
d. 7.6 ⫻ 105, e. 3.6 ⫻ 106,
and f. 2.8 ⫻ 107.
Light behaves like waves when it travels in empty space, and like
particles when it interacts with solid matter. Figure 38.5 is a striking
example of the particle nature of light. The photograph was taken with
exceedingly feeble light. Each frame shows the image progressing photon by photon. Note also that the photons seem to strike the film in an
independent and random manner.
......
Show the actual photoelectric
effect by placing a freshly
polished piece of zinc on a
charged electroscope and
illuminate it with an open
carbon arc lamp (no glass
lens). To focus the beam,
use a quartz lens (it will
transmit UV radiation). Show
that a positively charged
electroscope will not lose
its charge when the light
shines on the zinc plate,
but a negatively charged
electroscope will quickly
discharge in the same light.
Electrons are ejected from
the zinc surface. Block UV
with a glass plate and the
discharge ceases. Go further
if you have a quartz prism
and pass the light through a
slit, then through the prism,
and onto the zinc. Show
that the negatively charged
electroscope discharges only
when the portion of the
spectrum beyond the violet
end strikes the zinc plate.
CONCEPT What causes light to behave like a wave?
CHECK
Like a particle?
......
The photoelectric
effect suggests that
light interacts with matter as a
stream of particle-like photons.
CONCEPT
CHECK
Teaching Resources
• Problem-Solving Exercises
in Physics 19-2
• Laboratory Manual 100
a
b
c
d
e
f
38.4 Waves as
Particles
......
Light behaves like
waves when it travels
in empty space, and like particles
when it interacts with solid
matter.
CONCEPT
CHECK
770
770
38.5 Particles as
38.5 Particles as Waves
Waves
Common Misconception
If something is a wave, it can’t be a
particle, and vice versa.
If waves can have particle properties, cannot particles have wave
properties? This question was posed by the French physicist Louis
de Broglie in 1924, while he was still a student. His answer to the
question earned him a Ph.D. in physics, and later won him the Nobel
Prize in physics.
FACT Waves can exhibit
characteristics of particles
and particles can exhibit
characteristics of waves.
A beam of electrons
behaves like a beam of
light. a. The diffraction
of an electron beam produces an interference
pattern. b. The fringes
produced by a beam of
light are very similar to
those produced by the
beam of electrons.
a
b
De Broglie suggested that all matter could be viewed as
having wave properties. All particles—electrons, protons, atoms,
marbles, and even humans—have a wavelength that is related to the
momentum of the particles by
wavelength h
momentum
......
where h is, lo and behold, Planck’s constant again. The wavelength of
a particle is called the de Broglie wavelength. A particle of large mass
and ordinary speed has too small a wavelength to be detected by
conventional means. However, a tiny particle—such as an electron—
moving at typical speed has a detectable wavelength.38.5 It is smaller
than the wavelength of visible light but large enough for noticeable
diffraction. A beam of electrons, interestingly enough, behaves like a
beam of light. It can be diffracted and undergoes wave interference
under the same conditions that light does, as shown in Figure 38.6.
An electron microscope makes practical use of the wave nature
of electrons. The wavelength of electron beams is typically thousands
of times shorter than the wavelength of visible light, so the electron
FIGURE 38.7 microscope is able to distinguish details thousands of times smaller A scanning electron microscope
than is possible with optical microscopes. Figure 38.7 shows a fly’s
allows you to see this fly’s head
in striking detail.
head as seen with a scanning electron microscope.
CONCEPT
CHECK
What did de Broglie suggest about all matter?
Teaching Tip Give the
pronunciation of de Broglie as
duh-BRO-lee.
Teaching Tip Planck’s
constant surfaces again in the
de Broglie formula relating the
wavelength of a “matter wave”
to its momentum. Like light,
matter traveling through space
has wave properties. We don’t
ordinarily notice the wave nature
of matter, only because the
wavelength is so extremely small.
Teaching Tidbit Max Planck
was president of the Kaiser
Wilhelm Institute for Physics in
Berlin in 1930. Although Planck
remained in Germany while
Hitler was in power, he openly
protested the Nazi’s treatment
of his Jewish colleagues and
consequently was forced to
resign his presidency in 1937.
Following World War II, he was
reinstated as president, and the
institute was renamed the Max
Planck Institute for Physics in his
honor.
De Broglie suggested
that all matter could
be viewed as having wave
properties.
......
FIGURE 38.6
CONCEPT
CHECK
Teaching Resources
• Reading and Study
Workbook
• PresentationEXPRESS
• Interactive Textbook
CHAPTER 38
THE ATOM AND THE QUANTUM
771
771
38.6 Electron Waves
38.6 Electron Waves
If your students are
nonplussed by the wave–particle
duality, explain that we try to
interpret everything in terms
of what we see and experience
around us. What exists outside
our range of observation,
whether it be particles within
an atom or life forms in some
distant galaxy, may not fit our
expectations based on ordinary
experience.
Teaching Tip The possible
energy levels for an electron in
an atom can be compared to
steps on a staircase: One can rest
either on the third or fourth
step (level) but not on the
third-and-one-half stair (level).
There are no in-betweens.
(However, unlike stairs, atomic
energy levels are not evenly
spaced.)
FIRST
SHELL
SECOND
SHELL
FIGURE 38.8 In the Bohr model of the
atom, the electron orbits
correspond to different
energy levels.
Teaching Tidbit Louis
de Broglie’s doctoral thesis about
the wave nature of matter was
so radical that his professors
were uncertain about accepting
it. After asking Einstein about it,
and gaining Einstein’s approval,
the thesis was accepted. Five
years later de Broglie’s thesis won
him the Nobel Prize.
Bohr Model Explanation of Atomic Spectra An electron
can be boosted by various means to a higher energy level. This occurs
in gas discharge tubes, like those that make up neon signs. Electric
current boosts the electrons of the gas to higher energy levels. As the
electrons return to lower levels, photons are emitted. The energy of
a photon is exactly equal to the difference in the energy levels in the
atom. The characteristic pattern of lines in the spectrum of an element corresponds to electron transitions between the energy levels of
the atoms of that element. By examining spectra, physicists were able
to determine the various energy levels in the atom. This was a tremendous triumph for atomic physics.
One of the difficulties of this model of the atom, however, was
reconciling why electrons occupied only certain energy levels in the
atom—why, in effect, they were at discrete distances from the atomic
nucleus. This was resolved by thinking of the electron not as a particle whirling around the nucleus but as a wave.
De Broglie’s Theory
According to de Broglie’s theory of matter waves, electron orbits exist only where an electron wave closes
in on itself in phase. The electron wave reinforces itself constructively
in each cycle, just as the standing wave on a music string is constructively reinforced by its successive reflections. The electron is visualized
not as a particle located at some point in the atom, but as though its
mass and charge were spread throughout a standing wave surrounding the nucleus. The wavelength of the electron wave must fit evenly
into the circumferences of the orbits, as illustrated in Figure 38.9.
FIGURE 38.9 De Broglie suggested electrons have a wavelength.
a. Electron orbits exist only
when the circumference of
the orbit is a whole-number multiple of the wavelength. b. When the wave
does not close in on itself
in phase, it undergoes
destructive interference.
772
The planetary model of the atom developed by Niels Bohr, illustrated
in Figure 38.8, was useful in explaining the atomic spectra of the elements and why elements emitted only certain frequencies of light.
An electron has different amounts of energy when it is in different
orbits around a nucleus. An electron is said to be in a different energy
level when it is in a different orbit. The electrons in an atom normally
occupy the lowest energy levels available.
772
Teaching Tip The matter–
wave concept gives a clearer
picture of the electrons that
“circle” the atomic nucleus.
Instead of picturing them as tiny
BBs whirling like planets, the
matter–wave concept suggests
we see them as smeared standing
waves of energy—existing
where the waves reinforce, and
nonexistent where the waves
cancel (Figures 38.9 and 38.10).
FIGURE 38.10 In this simplified version of de Broglie’s theory
of the atom, the waves are shown only in circular
paths around the nucleus. In an actual atom, the
standing waves make up spherical and ellipsoidal
shells rather than flat, circular ones.
Teaching Tip Explain that
if the distance around the orbit
(the circumference) equals an
integral number of wavelengths,
then the orbits have the discrete
radii described by Bohr. The
paper-clip analogy in the text
illustrates this concept.
Both artists and scientists look for patterns in
nature, finding connections that have always
been there yet have
been missed by the eye.
According to
de Broglie’s theory
of matter waves, electron orbits
exist only where an electron
wave closes in on itself in phase.
......
The circumference of the innermost orbit, according to this
model, is equal to one wavelength of the electron wave. The second
orbit has a circumference of two electron wavelengths, the third
three, and so on. This is illustrated in Figure 38.10. Orbit circumferences are whole-number multiples of the electron wavelengths, which
differ for the various elements (and also for different orbits within
the elements). This results in discrete energy levels, which characterize each element. You can also think of a “chain necklace” made of
paper clips. No matter what size necklace is made, its circumference
is equal to some multiple of the length of a single paper clip.38.6 Since
the circumferences of electron orbits are discrete, it follows that the
radii of these orbits, and hence the energy levels, are also discrete.
This view explains why electrons do not spiral closer and closer
to the nucleus when photons are emitted. Since each electron orbit is
described by a standing wave, the circumference of the smallest orbit
can be no smaller than one wavelength—no fraction of a wavelength
is possible in a circular (or elliptical) standing wave.
In the still more modern wave model of the atom, electron waves
move not only around the nucleus, but also in and out, toward and
away from the nucleus. The electron wave is spread out in three
dimensions. This leads to the picture of an electron “cloud,” shown
previously in Figure 38.2.
CONCEPT
CHECK
Teaching Resources
• Reading and Study
Workbook
• Laboratory Manual 101
• PresentationEXPRESS
......
CONCEPT How did de Broglie’s theory of matter waves
CHECK
• Interactive Textbook
describe electron orbits?
CHAPTER 38
THE ATOM AND THE QUANTUM
773
773
38.7 Relative Sizes
38.7 Relative Sizes of Atoms
of Atoms
Common Misconception
The heavier the atom, the larger
its size.
The radii of the electron orbits in the Bohr model of the atom
are determined by the amount of electric charge in the nucleus.
For example, the single positively charged proton in the hydrogen
atom holds one negatively charged electron in an orbit at a particular
radius. In helium, with two protons in the nucleus, the orbiting electron would be pulled into a tighter orbit with half its former radius
since the electrical attraction is doubled. This doesn’t quite happen,
however, because the double-positive charge in the nucleus attracts
and holds a second electron, and the negative charge of the second
electron diminishes the effect of the positive nucleus.
FACT The heavier the atom,
the greater its nuclear charge
and the greater the number of
electrons in outer orbits. The
stronger electrical attraction
of the electrons to the nucleus
causes the heavier atoms to be
not much larger in diameter than
the lighter ones.
Teaching Tip Draw a model
of the hydrogen atom on the
board. Then place a second
positive charge in the nucleus
and explain that the force on
the electron will double. This
doubled force will pull the size
of the orbit (wave or particle)
in tighter. The double charge
will also hold an extra electron
and we have helium. So it is
understandable that helium is a
smaller atom than hydrogen
(no wonder it leaks so readily
through balloons!). Similarly,
uranium’s innermost orbits
(wave model or particle model)
are close to the nucleus, and
the uranium atom is only about
three times the diameter of the
hydrogen atom.
+1
+2
+3
+4
Hydrogen
Helium
Lithium
Beryllium
+10
Neon
FIGURE 38.11 Teaching Tip Mention that
elements shrink in size as one
goes from left to right in the
periodic table. Fluorine, for
example, is considerably smaller
than the atoms that precede it in
its row. Because of its smallness it
is able to penetrate the enamel
of teeth, and once inside, add
strength to the teeth like steel
girders strengthening a building.
The orbital model of the
atom is illustrated for some
light and heavy atoms. Note
that the heavier atoms are
not appreciably larger than
the lighter atoms.
774
774
+11
+12
Sodium
Magnesium
+80
Mercury
This added electron makes the atom electrically neutral. The two
electrons assume an orbit characteristic of helium. An additional proton added to the nucleus pulls the electrons into an even closer orbit
and, furthermore, holds a third electron in a second orbit. This is the
lithium atom, atomic number 3. We can continue with this process,
increasing the positive charge of the nucleus and adding successively
more electrons and more orbits all the way up to atomic numbers
above 100, to the synthetic radioactive elements.38.7
As the nuclear charge increases and additional electrons are added
in outer orbits, the inner orbits shrink in size because of the stronger
electrical attraction to the nucleus. This means that the heavier elements are not much larger in diameter than the lighter elements. The
diameter of the uranium atom, for example, is only about three hydrogen diameters even though it is 238 times more massive. The schematic
diagrams in Figure 38.11 are drawn approximately to the same scale.
The concept that an atom
can be understood only with
a mathematical model instead
of a simple physical planetary
model is very hard for high
school students to grasp. The
question “But what does it
look like?” is hard to leave
unanswered. “Like a wave cloud”
is a partial answer. The concept
of uncertainty that goes hand
in hand with quantum mechanics
is also a difficult one to accept.
Waves help here too, because a
wave has no fixed position.
FIGURE 38.12 The model of the atom has
evolved over time. a. In the
Bohr model, the electrons
orbit the nucleus like planets going around the sun.
b. De Broglie’s idea of a
wave following along an
orbit was an important
stepping stone toward the
current model. c. In the current model of the atom, the
wave model, the electrons
are distributed in a “cloud”
throughout the volume of
the atom.
The radii of the
CHECK electron orbits in the
Bohr model of the atom are
determined by the amount of
electric charge in the nucleus.
......
Each element has an arrangement of electron orbits unique to
that element. For example, the radii of the orbits for the sodium
atom are the same for all sodium atoms, but different from the radii
of the orbits for other kinds of atoms. When we consider all the elements, we find that each has its own distinct orbits.
The Bohr model of the atom solved the mystery of the atomic
spectra of the elements. It accounted for X-rays that were emitted
when electrons made transitions from outer orbits to innermost
orbits. Bohr was able to predict X-ray frequencies that were later
experimentally confirmed. He calculated the ionization energy of the
hydrogen atom—the energy needed to knock the electron out of the
atom completely. This also was verified by experiment. The Bohr
model accounted for the general chemical properties of the elements
and predicted properties of a missing element (hafnium), which led
to its discovery.
The Bohr model was impressive. Nonetheless, Bohr was quick to
point out that his model was to be interpreted as a crude beginning,
and the picture of electrons whirling like planets about the sun was
not to be taken literally (a statement to which popularizers of science
paid no heed). His discrete orbits were conceptual representations
of an atom whose later description involved a wave description. Still,
his planetary model of the atom with electrons occupying discrete
energy levels underlies the more complex models of the atom today,
which are built upon a completely different structure from that built
by Newton and other physicists before the twentieth century. This is
the structure called quantum mechanics. Figure 38.12 shows how the
model of the atom has evolved over time.
CONCEPT
think!
What fundamental force
dictates the size of an
atom?
Answer: 38.7
......
• Reading and Study
Workbook
• Problem-Solving Exercises in
Physics 19-3
• Transparency 92
CONCEPT What determines the radii of the electron orbits in
CHECK
Teaching Resources
• PresentationEXPRESS
the Bohr model of the atom?
• Interactive Textbook
• Next-Time Question 38-2
CHAPTER 38
THE ATOM AND THE QUANTUM
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38.8 Quantum
38.8 Quantum Physics
Physics
Key Terms
quantum mechanics,
quantum physics
The more that physicists studied the atom, the more convinced
they became that the Newtonian laws that work so well for large
objects such as baseballs and planets (in the “macroworld”) simply
do not apply to events in the microworld of the atom. Whereas in
the macroworld the study of motion is called mechanics, or sometimes classical mechanics, the study of the motion of particles in the
microworld of atoms and nuclei is called quantum mechanics. The
branch of physics that is the general study of the microworld of photons, atoms, and nuclei is simply called quantum physics.
While one can be quite certain about careful measurements in
the macroscopic world, there are fundamental uncertainties in the
measurements of the atomic domain. For the measurement of macroscopic quantities, such as the temperature of materials, the vibrational frequencies of certain crystals, and the speeds of light and
sound, there is no limit in practice to the accuracy with which the
experimenter can measure. But subatomic measurements, such as the
momentum and position of an electron or the mass of an extremely
short-lived particle, are entirely different. In this domain, the uncertainties in many measurements are comparable to the magnitudes of
the quantities themselves.
The subatomic interactions described by quantum mechanics are governed by laws of probability, not laws of certainty. This
notion is difficult for many people to accept. Even Einstein did not
accept this.38.8
If you continue to study physics, you will likely encounter quantum mechanics some time in the future. Scientists and philosophers
are still pondering the real meaning of quantum mechanics. It’s a
fascinating subject.
Teaching Tip Distinguish
between classical physics and
quantum physics: Classical
physics is primarily physics
before 1900 and involves the
study of familiar things such as
the forces, motions, momenta,
and energy of massive particles
that behave in a predictable
manner in accord with Newton’s
laws. For this reason classical
physics is often called Newtonian
physics. After 1900 it was found
that Newtonian rules simply
don’t apply in the domain of
the submicroscopic. This is the
domain of quantum physics,
where everything is “grainy”
and where values of energy,
momentum, position, and
perhaps even time, occur in
lumps, or quanta, all governed
by probabilities rather than
certainties.
Teaching Tip Clarify what
is meant by quantum (plural
quanta)—a quantity that occurs
or changes only in elemental
“lumps.” The total weight of
a bag of pennies is quantized
in the sense that its weight is a
whole multiple of the weight of
a single penny. Electric charge
is quantized, because the
charge on any body is a wholenumber multiple of the charge
of a single electron (quarks
notwithstanding). A chunk of
gold is quantized in that it is
made of a whole number of
gold atoms. Energy, angular
momentum, and perhaps even
time are composed of “lumps.”
Everything is made of “quanta.”
776
......
CONCEPT What laws govern the interactions described by
CHECK
quantum mechanics?
38.9 Predictability and Chaos
When we know the initial conditions of an orderly system we can
make predictions about it. For example, in the Newtonian macroworld,
knowing with accuracy the initial conditions lets us state where a planet
will be after a certain time, where a launched rocket will land, and when
an eclipse will occur. In the quantum microworld, we can give odds
where an electron is likely to be in an atom, and calculate the probability that a radioactive particle will decay in a given time interval.
Predictability in orderly systems, both Newtonian and quantum,
depends on knowledge of initial conditions.
776
......
The subatomic
interactions
described by quantum mechanics
are governed by laws of
probability, not laws of certainty.
CONCEPT
CHECK
......
Some systems, however, whether Newtonian or quantum, are not
orderly—they are inherently unpredictable. These are called “chaotic
systems.” Turbulent water flow is an example. No matter how accurately we know the initial conditions of a piece of floating wood as
it flows downstream, we cannot predict its location later downstream.
A feature of chaotic systems is that slight differences in initial conditions result in wildly different outcomes later. Two identical pieces
of wood just slightly apart from each other at one time are vastly far
apart soon thereafter.
Weather is chaotic. Small changes in one day’s weather can
produce big (and largely unpredictable) changes a week later.
Meteorologists try their best, but they are bucking the hard fact of
chaos in nature. This barrier to good prediction first led the scientist
Edward Lorenz to ask, “Does the flap of a butterfly’s wings in Brazil
set off a tornado in Texas?” Now we talk about the butterfly effect
when we are dealing with situations where very small effects can
amplify into very big effects.
CONCEPT
CHECK
Teaching Resources
• Concept-Development
Practice Book 38-1
38.9 Predictability
and Chaos
Teaching Tip Explain that
the science of chaos is not at
all “chaotic.” What makes it
interesting is that chaos has some
predictable features.
Teaching Tip Tell your
students to watch for the
tendency of junk scientists to
attribute anything weird to
quantum mechanics.
What determines predictability in orderly systems?
Physics of Sports
If you and a friend, sitting on snowboards at
the top of a perfectly
smooth ski slope, push
off from positions close
together with about
the same velocity, you’ll
follow similar paths and
end up near each other
at the bottom of the
slope. This is orderly
behavior. Small differences in conditions at
the beginning result
in small differences in
conditions at the end.
But if the ski slope is full
of hundreds of moguls
(bumps) you’ll likely find, after bouncing and jouncing down the slope, that you and your friend wind
up many meters apart—no matter how close your
initial conditions. This is chaotic behavior. Small
differences in conditions at the beginning are
likely to result in large
differences in conditions
at the end—so much so
that you can’t predict
where you’ll end up.
Interestingly, chaos is
not all hopeless unpredictability. If you and
your friend compare
notes after your rides
down the moguled
slope, you might find
that you had some very
similar experiences.
Maybe you skirted
around the sides of
many moguls in just the
same way. Maybe you
never went straight over
the top of a mogul. So there is order in chaos.
Scientists have learned how to treat chaos mathematically and how to find the parts of it that are
orderly.
Predictability in
orderly systems,
both Newtonian and quantum,
depends on knowledge of initial
conditions.
......
Chaos on the Slopes
CONCEPT
CHECK
Teaching Resources
• Reading and Study
Workbook
• PresentationEXPRESS
• Interactive Textbook
CHAPTER 38
THE ATOM AND THE QUANTUM
777
777
REVIEW
Teaching Resources
• TeacherEXPRESS
• Virtual Physics Lab 34
38 REVIEW
For: Self-Assessment
Visit: PHSchool.com
Web Code: csa – 3800
• Conceptual Physics Alive!
DVDs Atoms
Concept Summary
•
Through the centuries there have been
two primary models of light: the particle
model and the wave model.
•
•
The energy of a photon is directly proportional to the photon’s frequency.
The photoelectric effect suggests that
light interacts with matter as a stream of
particle-like photons.
Light behaves like waves when it travels
in empty space and like particles when it
interacts with solid matter.
De Broglie suggested that all matter could
be viewed as having wave properties.
According to de Broglie’s theory of matter waves, electron orbits exist only where
an electron wave closes in on itself in
phase.
The radii of the electron orbits in the
Bohr model of the atom are determined
by the amount of electric charge in the
nucleus.
The subatomic interactions described by
quantum mechanics are governed by laws
of probability, not by laws of certainty.
Predictability in orderly systems, both
Newtonian and quantum, depends on
knowledge of initial conditions.
•
•
•
•
•
•
778
••••••
778
Key Terms
••••••
quantum (p. 768)
photon (p. 768)
Planck’s
constant (p. 768)
photoelectric
effect (p. 769)
quantum
mechanics (p. 776)
quantum
physics (p. 776)
think! Answers
38.3
Not necessarily. The answer is yes if electrons are ejected by the high-frequency
light but not by the low-frequency light,
because its photons do not have enough
energy. If the light of both frequencies can
eject electrons, then the number of electrons ejected depends on the brightness of
the light, not on its frequency.
38.7
The electrical force.
ASSESS
38 ASSESS
Check Concepts
1. A visualization of a concept;
particle and wave
2. A granular or discrete unit;
charge of an electron, photon
of light
Check Concepts
••••••
Section 38.1
9. Does the photoelectric effect support the
particle model or the wave model of light?
1. What is a model? Give two examples for the
nature of light.
3. A photon
4. Basic constant of nature;
h 5 energy/frequency
5. Blue, higher frequency
6. Ejection of electrons in some
metals by light
Section 38.2
7. Violet light has more energy
per photon.
2. What is a quantum? Give two examples.
8. Yes, it has more photons.
9. Particle
Section 38.4
10. What causes light to behave like a particle?
Section 38.5
3. What is a quantum of light called?
4. What is Planck’s constant, and how does
it relate to the frequency and energy of a
quantum of light?
5. Which has more energy per photon—red
light or blue light?
Section 38.3
6. What is the photoelectric effect?
7. Why does violet light eject electrons from a
certain photosensitive surface, whereas red
light has no effect on that surface?
8. Will bright violet light eject more electrons
than dim light of the same frequency?
11. a. Do particles of matter have wave
properties?
b. Who was the first physicist to give a convincing answer to this question?
12. As the speed of a particle increases, does its
associated wavelength increase or decrease?
13. Does the diffraction of an electron beam
support the particle model or the wave
model of electrons?
10. Light behaves like a particle
when it interacts with solid
matter.
11. a. Yes
b. Louis de Broglie in 1924
12. Decreases, since momentum
increases
13. Wave model
14. Same
15. It can have only certain
energies.
16. Constructive interference for
allowed levels
17. Wave; only certain standing
wave patterns are allowed.
Section 38.6
18. Greater nuclear charge pulls
electrons tighter and closer
together.
14. How does the energy of a photon compare
with the difference in energy levels of the
atom from which it is emitted?
19. Greater nuclear charge pulls
electrons tighter and closer
together.
15. What does it mean to say that an electron
occupies discrete energy levels in an atom?
16. What does wave interference have to do
with the electron energy levels in an atom?
CHAPTER 38
38
CHAPTER
THE ATOM
ATOM AND
AND THE
THE QUANTUM
QUANTUM
THE
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20. Study of motion in the
microworld of quanta
21. Not at the same time; there
is always a fundamental
uncertainty.
22. Knowledge of initial
conditions
38 ASSESS
(continued)
Think and Explain
23. Diffraction, interference, and
polarization; photoelectric
effect
24. Bright red light may have
many photons and a great
amount of total energy, but
red light has too little energy
per photon.
17. Does the particle view of an electron or the
wave view of an electron better explain the
discreteness of electron energy levels? Why?
Think and Explain
••••••
23. What evidence can you cite for the wave nature of light? For the particle nature of light?
24. A very bright source of red light gives off
much more energy than a dim source of
blue light, but the red light has no effect in
ejecting electrons from a certain photosensitive surface. Why is this so?
25. UV photons are more
energetic than photons of
visible light.
26. Protons are held within an
atom’s nucleus and thus
proton ejection takes millions
of times more energy than
electron ejection.
27. a. Frequency determines the
kinetic energy of the ejected
electrons.
b. Brightness of the light
determines the number of
electrons ejected.
Section 38.7
18. Why is a helium atom smaller than a hydrogen atom?
19. Why are the heaviest elements not appreciably larger than the lightest elements?
28. No; white light is a mixture of
photons of many frequencies.
Section 38.8
29. Higher-frequency green light
20. What is quantum mechanics?
25. Why is it that for certain materials ultraviolet light induces the photoelectric effect and
visible light does not?
30. Ultraviolet light has the
highest frequency and
therefore a photon of it has
the greatest energy.
21. Can the momenta and positions of electrons
in an atom be measured with certainty?
26. Why does light striking a metal surface eject
only electrons, not protons?
27. a. In the photoelectric effect, does brightness or frequency determine the kinetic
energy of the ejected electrons?
b. Which determines the number of
ejected electrons?
31. Red light must have the
greater number of photons
to add up to the same energy
that the green light has.
32. Doubling the wavelength
of light halves its frequency.
Light of half its original
frequency has half the
original energy per photon.
33. Ultraviolet has the higher
frequency and so its photons
have greater energy. Cell
damage depends on the
energy of the individual
photons absorbed.
780
Section 38.9
22. What information is necessary to make predictions about an orderly system?
780
28. We speak of photons of red light and photons of green light. Can we speak of a single
photon of white light? Why or why not?
34. Lower speed means lower
momentum and longer
wavelength.
38 ASSESS
29. Which laser beam carries more energy per
photon—a red beam or a green beam?
30. Which photon has the most energy—one
from infrared, visible, or ultraviolet light?
31. If a beam of red light and a beam of green
light have exactly the same energy, which
beam contains the greater number of
photons?
32. If we double the frequency of light, we
double the energy of each of its photons. If
we instead double the wavelength of light,
what happens to the photon energy?
33. Suntanning produces cell damage in the
skin. Why is ultraviolet light capable of producing this damage while infrared radiation
is not?
34. Electrons in one electron beam have a
greater speed than those in another.
Which electrons have the longer
de Broglie wavelength?
35. a. The more-massive proton
has more momentum.
b. The electron with its
smaller momentum has the
longer wavelength.
36. Does the de Broglie wavelength of a proton become longer or shorter as its velocity
increases?
37. We do not notice the wavelength of moving
matter in our ordinary experience. Is this
because the wavelength is extraordinarily
large or extraordinarily small?
38. The equation E = hf describes the energy of
each photon in a beam of light. If Planck’s
constant, h, were larger, would photons of
light of the same frequency be more energetic or less energetic?
39. When do photons behave like waves? When
do they behave like particles?
40. A friend says, “If an electron is not a particle, then it must be a wave.” What is your
response? (Do you hear “either or” statements like this often?)
41. Why will helium leak through an inflated
rubber balloon more readily than hydrogen
will?
35. An electron and a proton travel at the
same speed.
a. Which has more momentum?
b. Which has the longer wavelength?
36. By de Broglie’s formula, as
velocity increases, momentum
increases, and thus
wavelength decreases.
37. Small; wave effects are
noticeable only when the
wavelength is comparable
to the size of obstacles and
openings.
38. More energetic, for photon
energy is directly proportional
to h. (The size of h determines
the scale of the quantum
world.)
39. Photons behave like waves
when in transit. They behave
like particles when being
emitted or absorbed.
40. We don’t know if an electron
is a particle or a wave. We
know it behaves as a wave
when in transit and behaves
as a particle when incident
upon a detector. It is an
unwarranted assumption that
it must be either a particle or
a wave.
41. Helium is smaller than
hydrogen—for two reasons.
A helium atom is smaller than
a hydrogen atom because
its electrons are more tightly
pulled in by the doublecharge nucleus. Helium gas
is also made up of single
atoms whereas hydrogen
gas is composed of diatomic
molecules (two atoms per
molecule).
Teaching Resources
• Computer Test Bank
More Problem-Solving Practice
Appendix F
CHAPTER 38
38
CHAPTER
THE ATOM
ATOM AND
AND THE
THE QUANTUM
QUANTUM
THE
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781
• Chapter and Unit Tests
781