Planck’s “quantum of action” from photoelectric effect
Task
To determine Planck’s quantum of action from the photoelectric voltages measured
at different wavelengths. Measure the I(U) characteristic of a photocell.
Principle
A potassium photocell is illuminated with light of different wavelengths. A photon of
sufficient energy can eject an electron from the cathode. An electron ejected by a
photon of frequency f leaves the cathode surface with the maximum kinetic energy
Ek  hf  A , where h is Planck’s quantum of action and A the work function from the
cathode surface (given by the material of the cathode). Some of these electrons
reach the unilluminated anode so that a voltage is set up between anode and
cathode. The electron can only run counter to the electric field if it has energy
Ek  eU , where e is the electron charge. Therefore after some (short) time the
voltage U reaches its limiting value eU  hf  A . Finally, we obtain the relationship
between the voltage U and the light frequency f :
h
U  f  const .
e
Repeating the measurement for several wavelengths, we obtain a linear function U(f)
as shown in Fig. 1 and we can determine the Planck’s quantum of action from its
slope.
Figure 1
Figure 2
We can also analyse the basic properties of a photocell using the apparatus of Fig. 2.
The outer source is used to create voltage to slow down the emitted electrons. If the
energy of photons incident on the cathode is high enough, and the potential
difference V will be set to zero, there will be a photoelectric current measured by the
picoammeter A. If we increase the potential the current will decrease, and when the
potential reaches a certain value, called the stopping potential U 0 , the current will
drop to zero. The kinetic energy of the ejected electrons is no more high enough to
overcome the voltage. It then holds: Ahf eU0 .
Equipment
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spectral lamp Hg with housing and set of 5 interference filters
power supply for spectral lamps
High-vacuum photo-cell for h-determination with housing
universal measuring amplifier, with screened cable, BNC, 30 cm
digital multimeter
picoammeter
variable resistor
universal source
connecting cords
Set-up and procedure
The experimental set-up for the first part of the measurement is as shown in Fig. 3.
The interference filters are fitted one after the other to the light entrance of the photocell.
Figure 3
The measuring amplifier is set to: electrometer Re  1013  , amplification 10 0 , time
constant 0; the multimeter is set to voltmeter DC 2V. A photocell must be discharged
via “zero” button of the measuring amplifier between the measurements (the shutter
on the photo-cell being closed).
1. Measure the limiting voltage for 5 different wavelengths.
2. Plot the measured points of a function U(f) as shown in Fig. 1.
3. Use the least squares method to determine the experimental line
U = a+ bf.
4. Calculate the value of h from its slope b as h=be.
5. Determine the confidence interval and compare the result with the literature
value.
The experimental set-up for the second part of the measurement is as shown in
Fig. 3. The photocell P is connected in series with the picoammeter A and the
variable resistor, on which we measure the voltage using the universal multimeter V
set to 2V DC. The variable resistor is attached to the universal source set to U = 2 V
DC. The same light-source as in the first part is used.
1. Change the photocell voltage U from 0 V to 1,5 V in steps of 0,1 V and
measure the current I through the photocell. Write the values in the table.
2. Plot a graph of I as a function of U. Apply linear regression to obtain the
approximate value of the stopping potential U 0 .
3. Calculate the work function of the cathode using the equation Ahf eU0 .