Physics 200 Class #13 Notes
October 19, 2005
Reading Assignment
Text: Chapter 6 pp. 141-160
Review of:
Electric Force - F (newtons, N)
Potential Energy - PE (joules, J)
Electric Field - E (newtons/coulomb, N/C)
"Electric Potential" - ""(volts, V)
You know that the electric field relates to the electric force through the equation E=F/q, but how
do force, electric field, potential energy, and "electric potential" relate?
kQq
kQ
(in units of newtons, N)
electric field E = 2 (newtons/coulomb, N/C)
2
r
r
kQq
kQ
Potential Energy PE =
(joules, J)
"electric potential" =
(volts, V)
r
r
NOTE: "electric potential" and potential energy are different things. You can think of electric
potential as the pressure pushing the electrons along - like pressure in a hose pushing water along.
If you have high pressure, you can have a spark across a large distance, if you have low pressure
you can only have a spark across a short distance.
electric force F =
definitions in terms of Energy:
Power (Energy/time)
Intensity or brightness (Power/area)
How bright are blackbody radiators - depends on temperature, and distance from object
watts
  5.67 x 108 2 4 )
(Power radiated R: R   T 4
m K
Much hotter stars than our sun look much dimmer. Why?
Phy 200 Fall 2005 Class_13
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Tonight, we review the Photoelectric Effect, discuss Compton Scattering
Chapter 6 The Photon
Is the wave theory of light enough to describe all phenomena in which it participates?
6.2 The photoelectric Effect
Einstein and the Photoelectric Effect
1. Collector positive: current flows
2. Collector negative: Current stops at some unique value
Major Problem with Wave Model: There is no time delay between the light turning on and the
ejection of photoelectrons! Classical theory predicts time delays of hours while the energy from
a wave builds up on the electron.
Recall from last time: Classroom demonstration of Photoelectric effect!
Key Points:
 No time lag between turning on light and photocurrent.
 Each frequency has a unique stopping voltage.
 Increasing the Intensity of the light does not change the stopping voltage
 There is a threshold frequency below which there is no effect.
The experimental facts are summarized by plotting stopping energy (voltage) versus frequency.
Typical curves are shown in the next figure.
Phy 200 Fall 2005 Class_13
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Interpretation:
1) The stopping voltage is a measure of the maximum kinetic energy of the ejected electrons.
2) The kinetic energy of the electrons is directly proportional to the frequency.
3) The threshold frequency indicates that the incident light must have a minimum energy to eject
electrons.
Einstein’s Interpretation:
The light is quantized (photon) and has energy directly proportional to its frequency!
 Maximum energy of   slope of 
 a constant that depends 


 f 

 electron after escape   graph line 
 on the material

KEmax  hf  W
eVS  hf  W
VS 
h
W
f
e
e
or
VS 
h
h
f  f threshold
e
e
W is the (Work Function): Minimum energy needed to remove electron from surface. This is a
unique value for each metal.
A new energy unit: The electron volt
If we measure the stopping voltage in volts, we convert to joules by multiplying by the charge on
the electron. One volt is equal to one joule/coulomb. The joule is an inconvenient unit to use in
atomic physics.
We usually specify the wavelength rather than the frequency:
hc
KEmax  hf  W 
W

KEmax 
1240eVnm

W
Example :Suppose  =500nm and W=1.2eV
1240eVnm
KEmax 
 1.2eV  2.48  1.2  1.28eV
500nm
It would take 1.28 volts to stop the electrons.
Phy 200 Fall 2005 Class_13
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6.3 The Compton Effect
Quick review of momentum: mv
The discovery of x-rays and their interaction with matter gives further evidence for the photon
picture of light and also allows us to confirm that photons carry linear momentum. The scattering
of x-rays from electrons allows us to determine the momentum of the photon. The “picture” of
Compton Scattering (Compton Effect) is shown below.
Production of X-rays: High speed electrons are shot into a metal and are rapidly accelerated
(decelerated). Accelerating charges produce radiation.
We apply Conservation of energy and conservation of momentum:
Conservation of energy:
energy of photon before + kinetic energy of electron before = energy of photon after + kinetic energy of electron after
hfbefore  zero  hf after  (kinetic energy of recoiling electron)
So when the photon scatters, it loses energy and gives this energy to the electron. This means that
it changes frequency (and wavelength) when it scatters. For example, green light hitting an
electron may scatter off as red light, which has lower energy.
Conservation of linear momentum:
The calculation is a bit more complicated here, but analysis shows that the linear momentum of the
photon can be written as follows:
hf
( Momentum of photon) 
c
or
h
( Momentum of photon) 

So remember - photons have energy, and have momentum. They can push things around, like
kicking electrons off of atoms.
Phy 200 Fall 2005 Class_13
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Questions from Chapter 6 (p. 160)
1. A certain metal surface ejects electrons when illuminated with green light but none when struck
by yellow light. Do you expect that electrons will be able to escape when the surface is illuminated
(a) by red light? (b) by blue light? Explain your reasoning.
2. A good mirror reflects about 80 per cent of the light energy that strikes it. How could you
distinguish experimentally between the following two possibilities: (a) 20 per cent of the photons
are not reflected; (b) all the photons are reflected but each with 20 per cent less energy?
3. If an electron in metallic cesium absorbs a photon of red light (specifically, λ = 6.6 x 10-7 meters
in vacuum), all the energy is used up in escaping from the attractive forces in the metal. There is
no energy left over after the electron has gotten out (just barely). Suppose blue-green light (with
λ = 5 x 10-7 meters) is used. What percentage of the photon's energy does the electron retain after it
has escaped from the metal?
(Recall that a photon's energy is determined by the frequency of the light. You can, however,
readily convert wavelength information into frequency information. If you do some algebra, you
will find that Planck's constant cancels out in the final answer. That will save you some nasty
multiplying - and you will see things more clearly.)
4. Some photographic materials can be handled safely in red light but are spoiled instantly when
white light is turned on. How might you account for this?
5. More about the photoelectric effect. The text never addressed the question of why some
electrons have less energy after escape than others. Suppose zinc is illuminated with ultraviolet
light of a single frequency, for example, f =1.5 threshold. Why might some electrons emerge with
less energy than "maximum energy of electron after escape"?
Phy 200 Fall 2005 Class_13
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