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Physics 200 Class #11 Notes
Reading Assignment



October 12, 2005
Text: Chapter 6 pp. 141-160
Reminder: The MidTerm Exam is on October 17
An introduction to The Photoelectric Effect (30 min.)
Review of the first 5 chapters (60 min.)
We now come to one of the first crucial problems of the early twentieth century.
Three types of Spectra:
1. Continuous (Blackbody Radiation)
2. Line Spectra
3. Absorptiion Spectra
Max Planck and Incandescent Radiation
Incandescent Radiation, Cavity radiation, Blackbody Radiation and Thermal radiation are all the
same.
The experimental facts: We plot the power radiated per unit area at each temperature. Note that the
temperature must be the absolute temperature in Kelvins. To convert from centigrade, add 273.
TKelvin = TCentigrade + 273.
So, 0 degrees C = 273K
and 3727 oC = 4000K
(notice you don't have to use the degrees symbol o for Kelvin)
R(λ) is the energy radiated per unit area per unit time. Notice the visible region.
(1) We find that the total power/area over all wavelengths (area under the curve) is given by:
watts
R  T4
  5.67 x 108 2 4
m K
In other wards, if we double the temperature, the power radiated increases by 16 times!
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(2) The peak of the curves is described by Wien’s Law which says that the product of wavelength
and temperature is a constant. This is a very useful relationship, especially in Astronomy.
maxT  constant  2.9 x10-3meterKelvin
You saw the light bulb change color with different temperatures. Here are some more examples this is how they tell the temperature of stars!
Spectra for actual stars, from zebu.uoregon.edu There's a vertical offset so the spectra don't
overlap so you can actually look at them. The top spectrum is for a star with temperature of about
7000K. The temperatures of the stars are lower as you go down, until the bottom spectrum is of a
star at about 4000K. The star labeled G12V is "solar like". That means, this is pretty much what
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the sun looks like. The curves are a bit messy because some light gets absorbed by gasses out in
space and around the stars themselves. Note though that the peaks of the curves move to longer
wavelengths for cooler stars.
Problem: The peak of the blackbody curve is measured to be at 1000 nm for a temperature of 2900
K. Find the temperature of the surface of the sun if the peak of the solar spectrum is at 500 nm.
And now, the beginning of quantum mechanics:
All attempts to predict the blackbody curve using classical physics failed except for very high
wavelengths (ultraviolet catastrophe). Planck was able to predict the curve by making some
assumptions about the energies of the atomic oscillators emitting the light.
Planck’s Assumption: The energy of the oscillators emitting the light is not continuous but is
quantized. If an oscillator is vibrating at a frequency f its energy can only have values given by
E  nhf
where n  1, 2 , 3, 4,...
Where h is a constant that must be determined experimentally. You will do this in Lab #7. The
units must be
joule x seconds.
h  6.626 x1034 joule  sec
 4.136 x1015 electron volt  sec
With this hypothesis, Planck introduces the notion that the Energy of a system is quantized
(comes in discrete fixed sizes). This might be considered one of the beginnings of quantum
mechanics.
(Remember the standing waves on a string - only certain frequencies were allowed (f, 2f, 3f, 4f ...).
This is the same principle.)
A nice Java Applet on Blackbody radiation:
http://physics.ius.edu/~kyle/physlets/thermo/blackbody.html?textBox=300
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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.
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.
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.
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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 eV
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.
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Quick review of quantitative concepts (Chapters 1-5 only):
General:
v velocity
wavelength
f frequency
x  x1
average velocity  vave  2
t 2  t1
velocity of light in a vacuum: c = 3x108m/s
 2 
Sine wave: y  A sin 
x
  
Diffraction: (light bending when moving between different materials)
n index of refraction
n=c/v
(light moves more slowly in materials with a higher index of refraction)
so... velocity of light in material: v=c/n
v=f
When moving through different materials, frequency stays same but wavelength changes.
v c

 
f n f
Think of the rows of marching soldiers walking off of grass into mud, they move more slowly and
pile up on each other.
sin 1 n 2

which you can write n1 sin 1  n2 sin 2
sin  2 n1
 is the angle from the "normal"
Snell's law:
example: for light moving from air to water, coming in at some angle air,
you can write nair sin  air  nwater sin  water
Light behaving like a wave:
Diffraction: the bending of light around corners. Do particles do that?
Interference:
y
 m
Maxima
L
Path Difference = λ Produces constructive interference
Path Difference = λ/2 Produces destructive interference
Double Slit: d sin   m
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[Also good for Diffraction Grating]
Electricity and magnetism:
Electric force on something that has charge:
F=qE
Electric force on something that has charge and is moving:
F=qvB if v is perpendicular to B, plus a direction given by the right hand rule.
For Blackbody Radiation (also called thermal radiation, incandescent radiation, cavity radiation, ...)
Total energy radiated: R   T 4
  5.67 x 108
watts
m2 K 4
The peak intensity: maxT  constant  2.9 x10-3meterKelvin
where n  1, 2 , 3, 4,...
quantum oscillator states: E  nhf
Only certain frequencies allowed. Like standing waves on a string, only multiples of the
fundamental frequency can be there.
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Definitions: work, energy, potential energy, kinetic energy
Kinetic energy is proportional to v 2
Momentum is proportional to v
Force
Momentum
Conservation of momentum
Energy
Potential Energy
Kinetic Energy
Conservation of energy!
collisions
elastic - all the energy goes into the bounce and nothing is crushed/smashed/etc. Energy stays in
the bouncing system. "Kinetic energy stays the same" The ball bounces back up.
inelastic - things go splat. energy is put into heating up the environment instead of only into the
bounce. "Kinetic energy does not stay the same", you lose kinetic energy. The paper wet paper
towel does not bounce back up.
Units in the metric system
Length: meter m
Mass: kilogram kg
Time: second s
Frequency: hertz Hz = 1/s
Velocity:
m
s
Acceleration:
m
s2
Force: newton N=
kgm
s2
kgm 2
Energy: joule J = Nm =
s2
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