Download The Photoelectric Effect

The Photoelectric Effect
Aims
The aims of this experiment are to demonstrate the photoelectric effect, observe its dependence on the
frequency of incident light, and to use experimental data to obtain a measured value of Planck’s constant,
h.
Introduction
The apparatus used to observe of the photoelectric effect is illustrated schematically below.
Measuring
amplifier
photocell
Incident light
CASSY input A
CASSY input B
Counter
voltage box
Figure 1
Monochromatic light (in this case produced by a broadband mercury lamp passing through a wavelengthselective interference filter) is incident on the cathode K of the photocell. This is typically made from
potassium. This causes electrons to be liberated from the cathode, which then flow to ground via the
anode, producing an electrical current. One of the key results of the photoelectric experiment is that no
current is detected unless the frequency of the incident light exceeds a certain threshold value, f0. For f<f0,
no photoelectrons are emitted, no matter how much the intensity of the light is increased. However, when
f>f0, the photocurrent increases proportionally with the intensity of the light. These observations are
inconsistent with a classical wave model of light, and led Einstein to postulate in 1905 that in these
circumstances light is behaving as a stream of particles (photons), with each photon having energy hf. For
further details see PHY102 lecture notes or any first year textbook.
Energy conservation in the photoelectric effect
The free electrons in the potassium cathode have a range of kinetic energies, similar to the energy
distribution of an ideal gas. The energy required to remove the most energetic electrons from the cathode
is known as the work function of the metal. When light of frequency f is incident on the cathode, the
maximum energy of the emitted photoelectrons is therefore given by:
E max
hf
(1)
Question: If the work function of potassium is 2eV, what would be the maximum wavelength of incident light for which the
photoelectric effect would be observed?
This maximum energy of the emitted photoelectrons can be determined by the counter voltage method
(figure 1). By applying a negative voltage to the anode with respect to the cathode, emitted photoelectrons
experience a repulsive force which reduces the flow of electrons from cathode to anode and therefore the
measured photocurrent. If the negative counter-voltage is increased sufficiently, the photocurrent reduces
to zero. The minimum voltage at which this occurs is known as the stopping voltage V0.
At this point, even the most energetic electrons are unable to overcome the repulsive electric field. Thus:
E max
(2)
eV0
and therefore:
eV0
(3)
hf
Question: If measurements of V0 were taken as a function of f, how would you plot the data to obtain values of h and ?
Experimental Setup
NB: PLEASE DO NOT TOUCH THE GLASS SURFACE OF THE PHOTOCELL, AND DO NOT
TOUCH THE SURFACES OF THE INTERFERENCE FILTERS OR REMOVE THEM FROM
THE FILTER WHEEL.
Figure 2
Mercury
lamp
Iris
Lens
Photocell
1) The apparatus should be already set up as shown in figure 2: if not, consult a demonstrator. Set the
iris to be about 1cm in diameter, and adjust the positions of the lens and the photocell so that the
light from the mercury lamp forms a spot of about 1cm diameter in the centre of the photocell.
Make sure that no light from the lamp falls on either the anode (the thin circular silver-coloured
wire inside the photocell) or the cathode connection (the short, thicker, dark wire at the back of the
photocell).
2) Place the cover on the photocell (fig 3a) and adjust its position so that light falls approximately
centrally on the entrance port
3) Place the filter wheel next to the photocell so that the central part of the iris connects to the cover
of the photocell to exclude as much stray light as possible (fig 3b). You might have to adjust the
position of the cover slightly to achieve a good fit.
4) The photocell and counter voltage box should already be correctly connected. If in doubt, please
consult Prof. Cockburn or Dr Collins.
Fig 3b
Fig 3a
5) Rotate the filter wheel so that the 405nm filter is in position, with the yellow lever on the filter
wheel iris diaphragm in position “A”.
6) Make sure the counter-voltage box initially has its switch in the “Reset” position. This sets the
counter-voltage to approximately -3V. Move the switch to the “Run” position: this causes the
negative voltage to gradually decrease. Record the variation in photocurrent as a function of
voltage on a computer using the CASSY interface (see Appendix).
7) Repeat the measurement for the 405nm filter with the iris lever in position “B” then do the same
for position “C”.
8) Record the stopping voltage V0 for the 405nm light. Take V0 to be the voltage at which the i-v
curves for the three different light intensities intersect.
9) Repeat steps 5)-8) for the 3 remaining filters.
10) Plot your data in an appropriate way to obtain values of h and
errors (use Excel/LINEST)
with associated experimental
Discuss whether the qualitative form of the i-v curves and their dependence on light wavelength and
intensity are consistent with the predictions of the photon model of light.
Consider how your measured values of h and
reasons for any discrepancies.
compare with expected values and discuss possible
SAFETY NOTES
The high pressure mercury lamp also emits light in the UV range, and thus excessive exposure can
damage the eyes and irritate the skin.
Never look into the direct or reflected beam of light from the mercury lamp
Do not expose the skin to light from the mercury lamp for more than a few minutes.
J Cockburn/S Collins, April 2008
Appendix: Use of “CASSY Lab” Software
1) Open CASSY programme from shortcut on desktop.
2) Press F3 to open window “My Documents” – select “Planck’s Constant”. This opens a graph
display and 2 windows showing the counter voltage and the output voltage from the measuring
amplifier (proportional to the photocurrent).
3) Set the switch on the counter-voltage box to “reset”
4) Move the counter-voltage switch to “Run” and start the data logging by pressing F9 or clicking
the “stopwatch” icon. Observe the photocurrent displayed on the graph as the counter voltage is
decreased.
5) When the maximum current has been reached, press F9 (or click stopwatch) again and reset the
counter-voltage back to maximum for the next measurement. After the 3 varying intensity
measurements have been made for a particular wavelength, print out the graph (click on the
appropriate icon). Right-clicking on the axes allows the scale to be changed as appropriate.
6) Save your data by pressing F2: save in your personal filestore with a filename referring to the
wavelength used.
Repeat steps 2-6 for all four wavelengths. When the dialogue box asks if you want to load a new
measurement series in addition to the present one, choose “no” and close the “Settings” window.