Physics
Particles and Waves
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
 Atomic physics and quantum effects
 Photons, the photoelectric effect, Compton
scattering, x-rays
 Students should know the properties of photons,
so they can:
 Relate the energy of a photon in joules or
electron-volts to its wavelength or frequency.
 Relate the linear momentum of a photon to its
energy or wavelength, and apply linear
momentum conservation to simple processes
involving the emission, absorption, or
reflection of photons.
 Calculate the number of photons per second
emitted by a monochromatic source of
specific wavelength and power.
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
 Atomic physics and quantum effects
 Photons, the photoelectric effect, Compton scattering, xrays
 Students should understand the photoelectric effect, so they
can:
 Describe a typical photoelectric-effect experiment, and
explain what experimental observations provide evidence
for the photon nature of light.
 Describe qualitatively how the number of photoelectrons
and their maximum kinetic energy depend on the
wavelength and intensity of the light striking the surface,
and account for this dependence in terms of a photon
model of light.
 Determine the maximum kinetic energy of photoelectrons
ejected by photons of one energy or wavelength, when
given the maximum kinetic energy of photoelectrons for a
different photon energy or wavelength.
 Sketch or identify a graph of stopping potential versus
frequency for a photoelectric-effect experiment, determine
from such a graph the threshold frequency and work
function, and calculate an approximate value of h/e.
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
 Atomic physics and quantum effects
 Photons, the photoelectric effect, Compton
scattering, x-rays
 Students should understand Compton scattering,
so they can:
 Describe Compton’s experiment, and state
what results were observed and by what sort of
analysis these results may be explained.
 Account qualitatively for the increase of photon
wavelength that is observed, and explain the
significance of the Compton wavelength.
 Students should understand the nature and
production of x-rays, so they can calculate the
shortest wavelength of x-rays that may be
produced by electrons accelerated through a
specified voltage.
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
 Atomic physics and quantum effects
 Wave-particle duality
Students should understand the concept of
de Broglie wavelength, so they can:
 Calculate the wavelength of a particle as a
function of its momentum.
 Describe the Davisson-Germer
experiment, and explain how it provides
evidence for the wave nature of electrons.
Table of Contents
1. The Wave-Particle Duality
2. Blackbody Radiation and Planck’s Constant
3. Photons and the Photoelectric Effect
4. The Momentum of a Photon and the Compton Effect
5. The De Broglie Wavelength and the Wave Nature of
Matter
6. The Heisenberg Uncertainty Principle
Chapter 29:
Particles and Waves
Section 1:
The Wave-Particle Duality
Wave-Particle Duality
 When a beam of
electrons is used in a
Young’s double slit
experiment, a fringe
pattern occurs, indicating
interference effects.
 Waves can exhibit
particle-like
characteristics
 Particles can exhibit
wave-like
characteristics.
29.1.1. A beam of electrons is directed at two narrow slits and the
resulting pattern is observed on a screen that produces a flash
whenever an electron strikes it. What is the most surprising
observation that is made in this experimental apparatus?
a) The electrons do not all strike the screen at the same location.
b) The electrons produce flashes on the screen.
c) The pattern on the screen is an interference pattern.
d) The shadow of the two slits is observed on the screen.
e) The electrons produce the same pattern on the screen with or
without the slits in place.
29.1.2. Which one of the following experiments demonstrates the wave
nature of electrons?
a) Small flashes of light can be observed when electrons strike a special
screen.
b) Electrons directed through a double slit can produce an interference
pattern.
c) The Michelson-Morley experiment confirmed the existence of
electrons and their nature.
d) In the photoelectric effect, electrons are observed to interfere with
electrons in metals.
e) Electrons are observed to interact with photons (light particles).
Chapter 29:
Particles and Waves
Section 2:
Blackbody Radiation
&
Planck’s Constant
Blackbody Radiation
All bodies, no matter how hot or cold,
continuously radiate electromagnetic
waves.
Electromagnetic energy is
quantized.
frequency
E  nf
n  0,1, 2, 3, 
Planck’s
constant
  6.626 10 34 J  s
29.2.1. Which one of the following processes occurs when a charged
atomic particle emits radiation?
a) The particle’s charge is reduced.
b) The particle turns into a light particle (photon).
c) The particle shows no physical changes.
d) The particle changes from a higher energy state to a lower energy
state.
e) The particle turns into a wave.
29.2.2. Upon which one of the following parameters does the
energy of a photon depend?
a) the mass of the photon
b) the amplitude of the electric field
c) the direction of the electric field
d) the relative phase of the electromagnetic wave relative to the
source that produced it
e) the frequency of the photon
29.2.3. Two quantum oscillator energy levels are 7.572 × 1019 J and
1.136 × 1018 J. Determine the frequency of the photon that is
emitted from this atom when a transition is made between these
two levels and determine n for the lower energy level.
a) 2.571 × 1014 Hz
b) 2.478 × 1014 Hz
c) 3.381 × 1014 Hz
d) 3.422 × 1014 Hz
e) 4.369 × 1014 Hz
Chapter 29:
Particles and Waves
Section 3:
Photons &
the Photoelectric Effect
Photons
Electromagnetic waves are composed of particle-like
entities called photons.
E  f
p 
Photoelectric Effect
 Experimental evidence
that light consists of
photons comes from a
phenomenon called the
photoelectric effect.
 The “Magic Brick Wall”
Photoelectric Effect
 When light shines on a metal, a photon can give up
its energy to an electron in that metal. The
minimum energy required to remove the least
strongly held electrons is called the work
function.
hf
 
Photon
energy
KE max

Maximum
kineticenergy
of ejected electron

Wo

Minimum
work needed to
eject electron
Graph of Kinetic Energy
KE max

Maximum
kineticenergy
of ejected electron
 hf
 
Photon
energy
Wo

Minimum
work needed to
eject electron
Example 2 The Photoelectric Effect for a Silver Surface
The work function for a silver surface is 4.73 eV. Find the minimum
frequency that light must have to eject electrons from the surface.
hf o  KEmax  Wo

0 J


Wo 4.73 eV  1.60 1019 J eV
15
fo 


1
.
14

10
Hz
34
h
6.626 10 J  s
Photoelectric Effect in Digital Cameras
Photoelectric Effect in Light Sensors
29.3.1. In the photoelectric effect experiment, what type of energy
process is occurring?
a) Kinetic energy is transformed into thermal energy.
b) Thermal energy is transformed into electromagnetic energy.
c) Radiant energy is transformed into kinetic energy.
d) Electromagnetic energy is transformed into thermal energy.
e) Radiant energy is transformed into potential energy.
29.3.2. Why can we not see individual photons, but rather light appears to us
to be continuous?
a) A light beam contains a multitude of photons, each with a very small
amount of energy.
b) The wave part of a photon superposes with the wave part of other photons
in the beam, making the beam appear to be continuous.
c) The wave part of the photon extends over a spatial region that is larger
than our eyes can detect.
d) The particle properties of photons do not interact with our eyes.
e) Each photon carries information from the whole electromagnetic
spectrum; and our eyes cannot interpret this information.
29.3.3. Consider the photoelectric effect experiment from the point of view
of classical (or Newtonian) physics. Which one of the following is not
one of the effects you would predict from a classical point of view?
a) There should be a measurable time delay between the time that light first
strikes the metal surface and the time when electrons are first emitted
from the surface of the metal.
b) The kinetic energy of the emitted electrons should vary linearly with the
frequency of light shining on the metal.
c) Light of any frequency shining on the metal surface should cause
electrons to be emitted.
d) The kinetic energy of the emitted electrons should increase
proportionately to the intensity of the light.
29.3.4. A special camera has been designed that opens and closes its
shutter for a very short time. A picture of an illuminated object is
taken with this camera. When the film is developed, only tiny, bright
dots appear randomly distributed on the picture. What does this
experiment tell us about the nature of light?
a) The dots are an interference pattern, which proves the wave nature of
light.
b) The small number of dots indicates that light waves were cut off by
the shutter as it closed.
c) The camera lens could not focus the light waves at a point on the film
with such a short time.
d) The random distribution of dots shows the particle nature of light.
29.3.5. When the photoelectric effect experiments were performed,
one effect was inconsistent with classical physics. What was it?
a) The kinetic energy of the ejected electrons did not vary with light
intensity.
b) The fact that electrons could form a current within a vacuum.
c) The kinetic energy of the ejected electrons increased as the
frequency of light increased.
d) The fact that light could free electrons from the surface of a metal.
e) The kinetic energy of the ejected electrons increased as the
wavelength of light decreased.
29.3.6. What was a surprising result of the photoelectric effect
experiments?
a) The electrons behaved like matter waves.
b) Below a certain frequency, no electrons could be ejected from the
metal surface.
c) Individual photons behaved like waves.
d) Above a certain light frequency, the current became zero amperes.
e) Light was proven to exhibit only a wave nature.
29.3.7. If light only had wave-like properties, you would not expect
there to be a cutoff frequency. Why is this true?
a) Only particles can eject electrons from a surface.
b) The energy of a wave does not depend on its frequency.
c) Light waves of lower frequency would still be able to eject
electrons.
d) An electromagnetic wave would be able to eject an electron from a
surface. It would just take longer.
e) None of the above answers are correct.
29.3.8. In an ideally dark room, a double-slit experiment is carried
out using a source that releases one photon at a time at a slow
rate. The observation screen in the experiment is replaced with
photographic film which provides a recording of the photons
striking it over time. After some time has passed, the film is
removed and developed into a photograph. What is observed
on the photograph?
a) two bright bands that correspond to the two slits
b) an interference pattern
c) a single bright band
d) It’s impossible to guess.
29.3.9. If a double-slit experiment is carried out using a source that releases
one photon at a time at a slow rate, an interference pattern may be
observed if the screen is replaced with photographic film. What
produces the interference?
a) Each photon interferes with the photons that have previously passed
through a slit.
b) Each photon interferes with the photons that pass through the slit after it.
c) Each photon interferes with all of the photons that ever go through the
slit.
d) Each photon interferes with itself.
e) Each photon interferes with the slit.
Chapter 29:
Particles and Waves
Section 4:
The Momentum of a Photon &
the Compton Effect
Momentum of Light?
 Arthur Compton directed
Xrays at a sample of
graphite, and found that
the frequency of the
scattered light was a
different frequency
 The scattered photon
and the recoil electron
depart the collision in
different directions.
 Due to conservation of
energy, the scattered
photon must have a
smaller frequency.
 This is called the
Compton effect.
Derivation of Compton Wavelength
E p , o  Ee , o  E p 



Energy is
conserved in the collision.
E p ,o  f o
Energy of
incident
photon
Initial
Energy of
electron
Energy of
scattered
photon
E p  f
Ee 
f o  me c  f 
 pe c 
Ee,o  mec
2
KineticEnergy
of recoil
electron
 pe c 
2
2
2
Ee


 me c

p c  f o  me c  f
2

2

2 2
Solve for (pec)2
2 2
e

 me c
 me2 c 4

2 2
Derivation of Compton Wavelength
p p ,o 

Momentum is
conserved in the collision.
pe  p p ,o  p p
Momentum
of incident
photon
pp

Momentum
of scattered
photon

p
e
Momentum
of recoil
electron
p e   p p ,o  p p 
2
p
p 2e   p p,o  p p   p p,o  p p 


p 2e  p 2p,o  p 2p  2 p p,o p p cos
c  f
pc 
2
f 

 f
p 2e c 2  p 2p,oc 2  p 2p c 2  2 p p,o p p c 2 cos
p 2e c 2   2 f o2   2 f 2  2 2 f o f cos
Derivation of Compton Wavelength

p c  f o  me c  f
2 2
e
2

2
 me2 c 4   2 f o2   2 f 2  2 2 f o f cos 
 A  B  C 2  A2  B 2  C 2  2 AB  2 AC  2 BC
f o 
2

 me c
  f 
2 2
2
 2f o me c 2  2 2 f o f  2fme c 2  me2 c 4
  f   f  2 f o f cos 
2
2
o
2
2
2
2f o me c 2  2fme c 2  2 2 f o f  2 2 f o f cos 
2f o me c 2  2fme c 2  2 2 f o f  2 2 f o f cos 
Divide both sides by 2hfofmec
c c

1 cos  
 
f f o me c
h
1 cos  
  o 
me c
Conceptual Example 4 Solar Sails and the Propulsion of Spaceships
One propulsion method that is currently being studied for interstellar
travel uses a large sail. The intent is that sunlight striking the sail
creates a force that pushes the ship away from the sun, much as wind
propels a sailboat. Does such a design have any hope of working and,
if so, should the surface facing the sun be shiny like a mirror or black,
in order to produce the greatest force?
29.4.1. A photon of wavelength Δ and frequency f strikes an electron
that is initially at rest. Which one of the following processes occurs
as a result of this collision?
a) The photon gains energy, so the final photon has a frequency greater
than f.
b) The photon loses energy, so the final photon has a frequency less than
f.
c) The photon loses energy, so the final photon has a wavelength less
than l.
d) The photon gains energy, so the final photon has a wavelength
greater than l.
e) The photon is completely absorbed by the electron.
29.4.2. An x-ray photon with an initial wavelength  strikes an
electron that is initially at rest. Which one of the following
statements best describes the wavelength of the photon after the
collision?
a) No photon remains after the collision.
b) The scattered photon’s wavelength will still be , but its frequency
will decrease.
c) The scattered photon’s wavelength will be longer than .
d) The scattered photon’s wavelength will be /2.
e) The scattered photon’s wavelength will be between /2 and .
29.4.3. X-rays with a wavelength of 0.10 nm are scattered from
an argon atom. The scattered x-rays are detected at an angle
of 85 relative to the incident beam. What is the Compton
shift for the scattered x-rays?
a) 0.0022 nm
b) 0.011 nm
c) 0.022 nm
d) 0.041 nm
e) 0.12 nm
Chapter 29:
Particles and Waves
Section 5:
The De Broglie Wavelength &
the Wave Nature of Matter
Wave Nature of Matter?
http://www.youtube.com/watch?v=DfPeprQ7oGc
The de Broglie Wavelength
The wavelength of a particle is given
by the same relation that applies to a
photon:
  p
Example 5 The de Broglie Wavelength of an Electron and a Baseball
Determine the de Broglie wavelength of (a) an electron moving at a speed
of 6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed
of 13 m/s.
h

6.63 10 J s 
p
 1.2 10
9.110 kg 6.0 10 m s
h p
34
31
6.63 10
6
34

Js
 3.3 10 34 m
0.15 kg 13 m s 
10
m
29.5.1. Estimate the de Broglie wavelength of a honey bee
flying at its maximum speed.
a) A honey bee cannot have a wavelength.
b) 2  1018 m
c) 5  1032 m
d) 4  1036 m
e) 1  1040 m
29.5.2. What is the de Broglie wavelength of a particle, such as an
electron, at rest?
a) The wavelength would be zero meters.
b) The wavelength would be infinitely small and not measureable.
c) This has no meaning. The de Broglie wavelength only applies to
moving particles.
d) Davisson and Germer measured this wavelength in their apparatus
and found it to be around 1010 m.
Chapter 29:
Particles and Waves
Section 6:
The Heisenberg Uncertainty
Principle
The Heisenberg Uncertainty Principle
Momentum and position

p y y  
4
Uncertainty in y component
of the particle’s momentum
Uncertainty in particle’s
position along the y direction
The Heisenberg Uncertainty Principle
Energy and time

E t  
4
Uncertainty in the energy
of a particle when the particle
is in a certain state
time interval during
which the particle is
in that state
Conceptual Example 7 What if Planck’s Constant Were Large?
A bullet leaving the barrel of a gun is analogous to an electron passing
through the single slit. With this analogy in mind, what would hunting
be like if Planck’s constant has a relatively large value?
29.6.1. Which one of the following statements provides the best description
of the Heisenberg Uncertainty Principle?
a) If a particle is confined to a region x, then its momentum is within some
range p.
b) If the error in measuring the position is x, then we can determine the
error in measuring the momentum p.
c) If one measures the position of a particle, then the value of the
momentum will change.
d) It is not possible to be certain of any measurement.
e) Depending on the degree of certainty in measuring the position of a
particle, the degree of certainty in measuring the momentum is affected.
29.6.2. The position along the x axis of an electron is known to be
between 0.31 nm and + 0.31 nm. How would the uncertainty in the
momentum of the electron change if the electron were allowed to be
between 0.62 nm and +0.62 nm?
a) The uncertainty in the momentum would be twice its previous value.
b) The uncertainty in the momentum would be half of its previous value.
c) The uncertainty in the momentum would not be affected by this
change.
d) The uncertainty in the momentum would be four times its previous
value.
e) The uncertainty in the momentum would be one fourth its previous
value.