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Photoelectric Effect - Get as DOC


									                              PHOTOELECTRIC EFFECT

I.     Introduction:
The photoelectric effect was discovered by Heinrich Hertz in 1887, in the same experiments in
which he produced and detected electromagnetic waves, thus confirming the predictions of Maxwell.
You have observed effects such as interference and diffraction of light, which are consistent with the
wave nature of light. However, the characteristics of photoelectric emission, in which light striking
a material causes electrons to be emitted if the frequency of the light is sufficiently high, do not seem
consistent with the predictions of the classical wave picture of light. In this wave picture, as the
intensity of light is increased the amplitude of the wave and the energy in the wave should increase
causing more energetic electrons, and larger numbers of electrons, to be emitted. Experimentally,
while the number of emitted photoelectrons increases with the incident light intensity, the maximum
kinetic energy of the emitted photoelectrons is observed to be independent of the intensity but does
depend on the frequency  (and on the wavelength  since  = c, the velocity of light). Einstein
provided an explanation (for which he received the Nobel prize in 1921) of the observations in terms
of the quantum picture of light first proposed by Planck in 1901 (for which he received the Nobel
prize in 1918). In this picture, light is composed of discrete quanta or packets of energy called
photons. Each photon has energy E = h, where h = 6.626x10-34 J·s is a fundamental constant of
nature called Planck's constant. When a photon of energy E = h is completely absorbed by an
electron in a metal, all of the energy of the photon is converted into kinetic energy K of the electron.
An amount of energy , called the work function of the metal, is required to free the electron from
the surface of the metal. Therefore, the emitted photoelectrons should have a maximum kinetic
energy Kmax = h  . If the light is incident on the emitter of a photocell, some of the
photoelectrons (charge e = 1.602x10-19 C) will normally reach the anode of the photocell and a
photocurrent will flow. If a reverse potential is applied, the photocurrent will reach a value equal to
zero when the reverse potential is equal to the stopping potential Vo, such that eVo = Kmax, and none
of the photoelectrons will have enough kinetic energy to reach the anode. Thus Vo = Kmax/e =
(h/e)  /e. The slope of a plot of stopping potential Vo versus frequency  of the photons should
be (h/e). You will measure the stopping potential Vo as a function of light frequency  and
determine h, Planck's constant. You will also investigate the dependence of the stopping potential
on the intensity of the light.

II.    Required Equipment:

PASCO h/e Apparatus, Mercury Light Source with Light Aperture and
Lens/Grating assemblies, Support Base and Coupling Bar assemblies,
Digital Multimeter (DMM), filters, stopwatch.III. Procedure:

The PASCO h/e Apparatus used in this experiment measures the stopping potential Vo directly. The
equipment should be set up as shown in the diagram below. Turn on the mercury light source (it will

take a while for it to “warm up”). Direct the light emerging from the lens/grating assembly onto the
slot in the white reflective mask of the PASCO h/e Apparatus. Connect the OUTPUT terminals of
the PASCO apparatus to the digital multimeter; make sure the meter is set to function as a voltmeter
and that your connections are to the right terminals for measuring voltage.

Look at the diagram at the right. Position
                                                                                          Window to
the h/e Apparatus directly in front of the                                         White Photodiode
Light Source. You should be able to see a                                                       Mask
sharp band of "white" light striking the      White
white reflective mask.          Shift the     Ref lective
Apparatus so the light falls squarely on      Mask
the opening in the mask. Roll the light
shield of the Apparatus (the black
cylinder between the reflective mask and
the box) to one side so you can see the
circular window in the box.           Look                                         Light Shield
through this window at the Photodiode                                              (show n tilted to
Mask in the back of the box. The band of      Base Support Rod                     the open position)
light should fall squarely on the pair of
black squares on this white mask. If the
band of light is not focused, or if it does
not fall squarely on the black squares, ask
your TA for help.

NOTE: The grating used in this assembly is "blazed" so the spectrum of light is brighter on one side
than the other. Make sure that the brighter spectrum is on a convenient side of your lab table.


A.    Stopping Potential as a Function of Light Frequency.

Return the Light Shield to the closed position. Rotate the position of the h/e Apparatus to one side
as shown in the first diagram. As you change the angle between the Light Source and h/e Apparatus,
you should be able to see five colored bands in the first-order Mercury light spectrum as the light
strikes the white reflective mask. The colors are, in order of decreasing frequency, ultraviolet
(appears as a blue line on the fluorescent reflective mask), violet (may appear more bluish), blue,
green, and yellow. Make sure you can see all five colored bands. (You can also see bands of a
second order spectrum at larger angles. Use only the first-order bands for measurements.)
Turn on the Digital Voltmeter (DVM). Turn the ON/OFF switch of the h/e Apparatus to ON.
Adjust the position of the Apparatus so the YELLOW band of light falls squarely on the opening in
the white reflective mask. No light from the other bands should strike the opening. Place the
YELLOW filter on the front of the mask.

Press and release the Discharge Button on the side of the h/e Apparatus. When the Button is
released, the DVM reading should rise to a maximum and remain fairly steady at the value of the
stopping potential Vo. Record the stopping potential. Repeat the process until you have at least
three values of the stopping potential for the yellow light. Remove the yellow filter and again
determine and record the stopping potential. Has the reading changed? If so, can you think of a
possible reason?
Adjust the position of the Apparatus so the GREEN band of light falls squarely on the opening in the
white reflective mask. Place the GREEN filter on the mask. Repeat the measuring process for the
stopping potential until you have at least three values.
Repeat the process for the other three colored bands until you have at least three values for the
stopping potential for each colored band. You do not need to use filters for these bands.

B.    Stopping Potential as a Function of Light Intensity.

Again adjust the Apparatus so that only one of the colored bands falls squarely on the opening in the
white reflective mask. If you select the YELLOW or GREEN band, be sure to place the
corresponding colored filter over the mask. The Variable Transmission Filter (VTF) has five
sections corresponding to transmissions of 100%, 80%, 60%, 40%, and 20% of the light. Place the
VTF on the front of the mask (and over the colored filter if one is used) so that the light passes
through the section marked 100%. Measure and record the stopping potential Vo as you did in Part
A. Start the stopwatch as you release the Discharge Button. When the DVM reading reaches its
maximum value, stop the stopwatch and record the time elapsed (the charging time).

Move the VTF so the light passes through the section marked 80%.             Repeat the process of
measuring the stopping potential and the charging time.
Repeat the previous step until you have readings of stopping potential and charging time for all five
sections of the VTF.
Repeat the entire procedure of Part B, using a different colored band.

IV. Analysis
The frequencies and wavelengths of the five bands of colored light are listed in the Table below.

               Color                  Frequency (Hz)                  Wavelength (nm)
               Yellow                 5.20/5.18  10+14                 577.0/579.0
               Green                  5.490  10+14                     546.1
               Blue                   6.879  10+14                     435.8
               Violet                 7.409  10+14                     404.7
               Ultraviolet            8.203  10+14                     365.5
A. Determine mean values of the stopping potential Vo from your measurements for each of the five
colors of light. Determine errors Vo for these mean values. This you can find from the data sheet
for the Extech Digital MultiMeter Model MT 310. ( You can find it on the internet or by )
 Plot the stopping potential Vo versus light frequency  for all five colors. Include vertical error bars
on your points. Draw the "best" straight line and two "worst acceptable" straight lines through the
points on your graph. Use these lines to determine the slope and the error in the slope. According to
the quantum picture of light in which Vo = Kmax/e = (h/e)  /e, the slope of the line should be h/e.
Use your measured value of the slope and its error and the accepted value of the electron charge e to
determine Planck's constant h and the error h in your value. Compare your value for h with the
accepted value. Are they consistent? Use the intercepts of your straight lines with the Vo axis to
obtain the work function  and its error for the emitting surface.

B. On another graph, plot the stopping potential Vo versus the light intensity (in %) for both of the
colors for which you have measurements. Draw a "best" straight line through the points for each
color. Are your results consistent with a stopping potential that is independent of the light intensity?

Questions for the report:
1. Describe the effect that changing the color (and frequency) of the light has on the stopping
   potential and thus the maximum kinetic energy of the photoelectrons.
2. Describe the effect that changing the intensity of a single color (and frequency) of the light has
   on the stopping potential and on the charging time after releasing the Discharge Button.
3. Discuss whether your results in this experiment support a wave picture or a quantum picture of
   light. In your own words, discuss how you interpret the idea that light may exhibit the
   characteristics of waves in some situations and the characteristics of quanta in other situations.
4. Discuss possible sources of error in your measurements. In what way would they affect your

NOTE: Before you leave the lab, all measurements must be complete and each lab partner must
have a complete data sheet initialed by your TA, including multiple measurements of stopping
potential as a function of light color for five colors of light and measurements of stopping potential
and charging time as a function of light intensity for two colors of light. If you have time, try to
make rough plots of your data before you leave the laboratory, to see if your measurements are

consistent with straight line relationships.


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