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THE PHOTO-ELECTRIC EFFECT
INTRODUCTION
This is one of the fundamental experiments of quantum physics. It utilizes
the phenomenon of photo-electric emission of electrons and provides a simple
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way to determine   , the ratio of Planck's constant to the electronic charge.
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The optical arrangement of the apparatus used is shown schematically in Figure
1. A picoammeter and a variable voltage source are also provided.
The equation of conservation of energy that describes the production of
photoelectrons is
Hv = Kmax + W
(1)
Where v is the frequency of the light incident on the photo-sensitive surface, Kmax
is the kinetic energy of the most energetic electrons emitted from the surface and
W is the work function of the surface. The emission of electrons from the
cathode produces a photo-current that can be measured with a picoammeter
(see Figure 2). If the anode is maintained at a negative potential V with respect
to the cathode, the photo-electrons will experience a retarding field. Thus as V is
changed the photo-current will be changed, and there will be some value Vs of
the anode potential which stops the most energetic electrons and reduces the
photo-current to zero. Thus.
Kmax = eVs
(2)
Combining equations 1 and 2
Vs 
h
W
v
e
e
(3)
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In principle then, by determining Vs as a function of v,   is obtained as the
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slope of the graph of Vs versus v.
THE EXTPERIMENTAL SET-UP
The apparatus is mounted on two optical benches. (See Figure 1 for a
schematic representation.) The first part of the apparatus consists of a mercury
lamp and some optical devices including a constant deviation prism to produce
dispersion of the mercury spectrum. When the light emerges from the prism the
mercury spectral lines are sufficiently dispersed so that any single spectral line
can be made to focus on the photo-cathode. By moving the first optical bench
with respect to the second the photocell can be exposed to a small portion of the
spectrum. Thus the apparatus should be set up to focus a spot of monochromatic light on the photo-sensitive surface. This spot should spread over a
sizeable region of the photo-cathode but should also be sufficiently small so that
light does not hit the anode ring. (The American Institute of Physics Handbook
lists the wavelengths and relative intensities of the mercury spectral lines.)
In setting up the apparatus the photocell should be kept in the light-tight
box until all adjustments are completed. Replace the photocell with a sheet of
paper while arranging the apparatus so that a spectral line is focused on the spot
where the photo-cathode will be. The photocell should never be exposed to any
light except under these experimental conditions. Room lights should be turned
off when the photocell is out of its box.
The apparatus should be arranged electrically as in Figure 2. The
Keithley 414A picoammeter is a sensitive ammeter which permits measurements
of currents, with a maximum sensitivity of 100 pA full scale. The "Bias Potential
Box" provides the stopping or accelerating potential to the anode. (The anode
can be made positive with respect to the cathode if A and C are interchanged.)
The voltage V is not simply the potential difference between anode and cathode
but includes some (small) voltage drop across the picoammeter - note that photo
currents will range between ~1 A and ~1pA.
Measure the photo-current as a function of retarding voltage. If there is a
back current, i.e., there is a current when the anode potential is more negative
than Vs, some corrections may have to be made in the data. This is discussed in
the Melissinos reference. You should obtain values for Vs for a number of
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spectral lines, and determine   using equation (3).
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SUBTLETIES
This experiment is in fact considerably more complicated than is implied in
the simple description above. It is probably a commendable achievement to
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obtain a value for   within 5% of the accepted value, although the total
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uncertainty in the experimental values is ~1%. A crucial difficulty with the
experiment is the anode current that almost always exists. (see e.g., "Evaluation
of Commercial Apparatus for Measuring h/e", Amer. Jour. Physics 34, 75 (1996)).
It is difficult to decide whether the best procedure is to attempt to eliminate this
reverse current, or to make some correction for it. You will have to put
considerable thought into how you assign a value of Vs from the V-I plots which
probably won't simply have I go to zero and stay there below some value of V.
Another difficulty lies in the choice of mercury spectral lines. When the
spectrum contains two or three closely spaced lines, it is the highest frequency
line (rather than the most intense line) that dominates the V-I plot in the region of
Vs. In fact, of course, the experimental V-I data is the sum of the photo-currents
produced by each line. This problem is greatly diminished when the most
intense line of the group is also the highest frequency line.
A common source of difficulty is electrical noise pickup. Careful separate
grounding of the cell housing and the bench reduces this noise. However, any
capacitive pickup by the unshielded part of the sensitive picoammeter lead will
produce problems.
Care of the photocell is an important aspect in the obtaining of good
results. Electrically conducting salts deposited on the glass surface by handling
may cause leakage currents. Also, light exposure may affect the work function of
the cathode surface, either reducing that work function or making the surface
non-uniform.
The real challenge of this experiment lies in understanding the many nontrivial processes that complicate the simple picture described by equation (1).
REFERENCES
Melissions, Experiments in Modern Physics
American Institute of Physics Handbook
"Evaluation of Commercial Apparatus for Measuring h/e", Amer. Jour. Physics
34, 75 (1996).