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Transcript
PHYS 212
Modern Physics Lab
Photoelectric Effect
Introduction
The photoelectric effect was discovered by Heinrich Hertz in the 1880's when he noticed that incident light
could cause the ejection of particles from the surface of a metal. This process was called photoemission. In
1880 light was believed to be completely wavelike in nature and fully described by James Clerk Maxwell's new
theory of electromagnetism--the famous "Maxwell Equations” --which clearly demonstrated that light was a
wave.
Some aspects of the photoelectric effect seemed impossible to reconcile with this wave view of light. For
example, the emission of particles from a surface in response to incident light depended on the frequency of the
light, rather than the intensity. According to the classical theory, incident light should be steadily absorbed by
the surface of the metal until enough energy had been absorbed to eject a particle. Hertz found that this was not
true; in fact, for some frequencies of light, no amount of radiation was sufficient to eject a particle while for
other frequencies any amount was sufficient. The photoelectric effect, along with the “ultraviolet catastrophe”
discovered in the study of blackbody radiation and Compton scattering eventually toppled the great classical
theory of electromagnetism and shook the foundations of classical physics.
In 1905 an unknown clerk in a Swiss patent office published a paper in which he explained the photoelectric
effect. He argued that light was not a wave--it was particulate--and it travels in little energy bundles called
photons. The energy of one of these photons is hf, where h is the fundamental constant of nature recently
proposed by Max Planck to explain blackbody radiation, and f is the frequency of the photon. This novel
interpretation of light turned out to be very significant and secured a Nobel Prize for its originator--Albert
Einstein.
The photoelectric effect together with the problem of blackbody radiation were the two experimental
foundations on which the theory of quantum physics was constructed. For this reason the photoelectric effect
can be considered one of the most important experiments in the history of physics. From an experimental point
of view the photoelectric effect is also significant because it can provide a numerical value for Planck's
constant.
Theory
In a metal many of the electrons are not bound to the atomic nuclei in the metal. These conduction electrons,
as they are called, move freely in the metal, and can act independently. If a conduction electron absorbs
enough energy it can overcome its attraction to the metal and is emitted from the surface. For most metals
there is a well-defined energy that must be absorbed by a conduction electron before it is emitted. This energy
is called the work function , since it is a measure of the amount of work that must be done on one of the
electrons to free it from the metal. The work is done against the electrostatic force which attracting the
electron to the metal.
When a photon strikes the surface of a metal, it imparts all of its energy to a conduction electron near the
surface of the metal. If the energy of the photo (hf) is greater than the work function, the electron may be
ejected from the metal. If the energy is less than the work function, the electron will simply acquire some
kinetic energy that will dissipate almost immediately in subsequent collisions with other particles in the metal.
It follows that the kinetic energy of the emitted electrons will depend linearly on the frequency of the incident
radiation, provided this frequency is high enough to overcome the barrier of the work function. Furthermore,
photoemission can occur immediately after the arrival of the photon. For light of the appropriate frequency, the
number of emitted electrons will be proportional to the number of incident photons--or the intensity.
You can test your understanding of this phenomenon by considering the following situation: it is known that
both blue light and red light can eject electrons from a certain metal. In an experiment in which the intensity of
both the blue light and the red light were precisely equal the red light was observed to eject more electrons than
the blue light. Why would that be?
As stated above, the minimum amount of energy required to free an electron is known as the work function of
the metal. If we express this work function, designated , in volts, the following photoelectric equation is
obtained:
Ee  hf  e
where
Ee
f

= the energy of the liberated electron,
= the frequency of the incident light, and
= the work function for the metal.
Now consider the case of electrons being emitted by a photocathode in a vacuum tube, as illustrated Figure 1.
Figure 1 – A schematic diagram of the photoelectric effect idea. Electrons are emitted from a
Photon
Photocathode
+
+ T0
+ electron
+
\-
Anode
V
photocathode when it is illuminated. Photons transfer energy to the electrons, which then lose energy
breaking free of the metal surface, and crossing the potential difference V between the cathode and
anode.
Consider the case when the applied potential has the polarity shown in Figure 1. In this case, all emitted
electrons are slowed down as they approach the anode, and some of their kinetic energy is converted into
potential energy. There are three possibilities, as shown in Figure 2.
The first is that if the potential is small then the potential energy at the anode is less than the kinetic energy of
the electrons and there is a current through the tube (Figure 2a).
The second is if the potential is large enough the potential energy at the anode is larger than the kinetic energy
and the electrons are driven back to the cathode (Figure 2b). In this case, there is no current.
Figure 2 – If the total energy of the electron is greater than the potential energy at the anode the electron
will reach the anode and a current will be recorded. If the total energy is smaller the electron will reverse
its motion and never reach the anode.
The third case is if the voltage just stops the current (or electrons). The voltage required to do this is called the
“stopping potential". Using the photoelectric equation we find
Ee  T  V  eV0 ,
so
eV0  hf  e
or
V0 
h
f  .
e
Finally, if we reverse the polarity of the voltage, rather than being repelled the electrons are attracted to the
anode. In this case, the current will increase with voltage until all of the electrons are collected, at which point
the current will plateau.
I. Experimental Apparatus
Figure 3 is a diagram of the physical layout of the experiment. Figure 4 is a photograph of the apparatus. In
Figure 5 you will find a block diagram for the electronics. You should study the diagrams carefully before you
try to assemble the equipment so that you will know what is going on. Make sure that you know which
terminal is the anode, what you are measuring with each of the meters, and what voltages are involved.
Information about the RCA 929 photodiode is given in the appendix.
Hg Light Source
Focusing Lens
Focusing Lens
Filter
RCA 929
Photodiode
Figure 3 – Physical layout of the apparatus showing the mercury light source, the glass safety filter, the
focusing lens, thre transmission filter, and the RCA 929 photodiode tube.
Figure 4 -- Photograph of the apparatus, showing the Hg light source, lens, photodiode and electronics.
Photocathode
8
+
+ RCA 929
+ Photodiode tube
+
\
-
Vernier Diff
Voltage Probe
+
GW
SFG2004
Function Gen
Anode
4
Keithley 6485
Picoammeter
Vernier Diff
Voltage Probe
Common
Ground
-
Figure 5 -- Block diagram of the electronics for the experiment. The function
generator provides a varying voltage that is recorded by the computer. The
current is monitored by the Keithley picoammeter.
Light is produced by the mercury light source via the excitation of atomic transitions in mercury. These
transitions produce intense light at several wavelengths, listed in Error! Reference source not found.. The
light is focused onto a small narrow band interference filter. Light of a particular wavelength is selected by
using the appropriate interference filter, which allows light of  10 nm from the central maximum to pass. A
small iris collimates the light so that the light passes only through the center of the filter and not the outer edge
that does not have the interference coating. The problem with this technique is the low light levels, which
results in a bad signal to noise ratio. Also, the output of the mercury lamp is not constant – the light flickers.
The retarding potential across the RCA 929 tube is provided by a GW Instek SFG-2004 Function Generator,
which produces a sinusoidal potential which varies very slowly with time. This voltage is monitored by Vernier
Differential Voltage probe on the LabPro interface. The current flowing through the phototube is monitored by
the Keithley 6485 Picoammeter that produces an output voltage on the back panel, proportional to the input
current. This voltage level is recorded by another differential voltage probe on the LabPro.
Note: The currents that you are measuring are very small. You can get a good idea of this by
calculating the actual number of the electrons that are flowing in your experiment. Stray electrical and
magnetic fields easily affect tiny currents like this. You will see that by moving your position it may be
possible to affect the current. Extreme care must be taken when measuring the current, since it is very small
and easily hidden by noise. Watch out for unshielded open loops of wire.
Note: It is possible to destroy the picoammeter if you are careless when you set it up. Make sure that
you know what it is that you are doing before you go connecting expensive pieces of equipment to each other.
DANGER: The Hg lamp emits ULTRAVIOLET RADIATION (UVC). Avoid exposure. Ultraviolet
radiation is harmful to the skin and the eyes and can cause serious skin burns and eye injury either from direct
or reflected radiation.
Table 1– A listing of the major spectral lines of
mercury produced by the Hg light source.
Hg Line
Spectrum
Intensity
Filter
Color
(nm)
(Angstroms)
(±10 nm)
2536
300000
ultraviolet
2967
2600
3126,3132
7500
313
3341
160
334
3650,3655
6270
365
4047
4400
405
violet
4348
34
4358
10000
436
blue
5461
10000
546
green
5770
1100
577
red
II. Experimental Procedure
Here is a rough idea of the procedure to follow.
A. Carefully set up the circuit shown in Figure 5. Take care with the picoammeter.
B. Set up the apparatus as shown in Figure 3 and focus the light so that it would pass through the filter and
strike the photocathode.
C. Insert a filter into the holder. Be careful not to put a fingerprint onto the surface.
D. Turn on the Hg light source. This is a low-pressure Hg source enclosed in a glass to be that absorbs the
most dangerous UV wavelengths and is safe for general use. Nevertheless, it is emitting UV so do not
look directly at the bulb. Avoid prolonged eye exposure. Make sure the lamp is turned off when not in
use.
E. Adjust the GW Function generator so that it is producing a sinusoidal wave with amplitude of about 6
Vpp and a frequency as low as possible.
F. Calibrate the LabPro voltage input that is reading current through the picoammeter so that the LabPro
will be plotting the correct current.
G. Set up LoggerPro so that you will be plotting the current versus the voltage produced by the Function
generator.
H. Collect a current versus voltage plot for each filter, and also one without a filter. Assume that the data
without the transmission filter and lens corresponds to 2536 Angstroms. (Why?) When you finish, you
should have plots similar to Figure 6.
III. Experimental Analysis
A. Plot the potential versus photocurrent for all the wavelengths measured.
B. For each graph determine the stopping potential. You will need to think about how to do this!
Forward photocurrent
Reverse photocurrent
Figure 6 -- Plot of photocurrent versus stopping voltage for several wavelengths of light on the photocathode.
The stopping potential is the voltage at which the current becomes “flat”. Obviously, the y-axis has not been
calibrated and should be measured in nA.
C. Estimate the uncertainties in your measurement of each stopping potential.
uncertainties in the measured frequencies?
What are the
D. Plot the stopping potential versus the frequency. Plot the error bars in your measured values.
h
f   to your data, and determine h and the work function . Estimate
e
the uncertainty in your results. See figure 7 for an example of such a plot.
E. Fit the theory line V0 
Figure 7– A plot of stopping potential as a function of frequency of incident light. This
plot should show the uncertainty in each measurement.
F. Does the shape of the measured response agree with theory?
G. Compare the values of h and  with previously measured values.
IV. Laboratory Report
1.
In your laboratory report be sure to include a detailed description of how you made your
measurement -- describe the apparatus and the procedure you used to make the measurement.
2.
You definitely should include a schematic diagram of the experiment as it actually was (i.e. don't
count on it being exactly what is in this lab handout.)
3.
You should have plots of current versus voltage for each of the wavelengths. You should also
have a plot of stopping potential versus frequency.
4.
You should determine a measured value (with uncertainty) for h and the work function.
5.
You should you should discuss the uncertainties present in your measurement.
V. Questions to ponder
1.
What is the work function of the cathode?
2.
How could the experimental error of the determination of Planck's constant be reduced?
3.
What are the cathode and anode made of? Melissinos gives the work functions of several metals.
From his discussion, can you figure out why your measured work function for the tube might
differ from the work function of the cathode alone?
4.
What is the threshold frequency of the tube? How is the threshold frequency related to the work
function?
5.
One of the challenges of this experiment is the measurement of the very small currents produced
in the phototube. Can you think of anything in the room where you did your experiment that
might have affected your measurement of these small currents?
6.
Why does the photocurrent go below zero? How could we eliminate this “reverse
photocurrent”?
7.
Why is the data from the Hg lamp assumed to correspond to 2536 Angstroms? Does the glass
envelope of the 939 tube affect this? How can you tell?
8.
How narrow is the range of frequencies produced by the Hg source/filter? How do you know the
values listed are correct?
Appendix A – RCA 929 Photodiode Specifications
Appendix B – 1P39 Photodiode Specifications
Appendix B – 1P40 Photodiode Specifications
Appendix C – UV-VIS transmission through glass
Optical Transmission - Soda Lime Glass
Optical Transmission - Borosilicate Glass (7052 / 7056)
http://www.sinclairmfg.com/nonflash/datasheets/optical3.html