Andrews University
Department of Physics
The Photoelectric Effect: Determining Planck’s Constant
A Lab Report
Presented in Partial Fulfillment
Of the Requirements of the Course
PHYS377: Advanced Lab 1
Erik Vyhmeister & Jeremy Thomas
Abstract
This experiment used the photoelectric effect and specific apparatus to determine the value of Planck’s
constant. A mercury lamp was used as the light source, and the energy of ejected electrons was determined by
the stopping potential created by their moving to the anode. The value of Planck’s constant was determined to
be within 0.25% of the accepted value, with a maximum uncertainty of +/- 5%.
Introduction
The purpose of this experiment is to determine Planck’s constant, h by using the photoelectric effect. The
photoelectric effect occurs when photons incident on a material (typically a metal) impart enough energy to the
highest-level electron, causing it to be ejected. The energy of the electron is modeled by the equation
𝐾𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 = ℎ𝑓 − 𝑊0
(1)
Where h is Planck’s constant, f is the frequency of the photon, and W0 is the work function – the amount of
energy it takes to get the electron out of its potential well.
Electrons with energy K
Photons
Metal
Figure 1. A visual demonstration of what the photoelectric effect looks like in action.
In the experiment, we measured the voltage needed to stop outgoing electrons for different specific frequencies
of light, thereby determining their energy in eV. From this, we will be able to determine the value of h by
rearranging (1).
ℎ
𝑉 = 𝑒∗𝑓−
𝑊0
𝑒
(2)
Since the stopping potential depends only on f, the slope should be h/e, and with a known value of e we can
determine h, Planck’s constant, which is crucial to much of quantum theory.
Description of Experiment
Equipment used:



PASCO AP-9368 (h/e apparatus)
Green, yellow filters
Voltmeter
The PASCO apparatus consists of a mercury lamp, which produces very specific frequencies of light. The light is
then passed through a diffraction grating to separate out the different colors (frequencies).
Mercury Lamp
Diffraction Grating
Target – cathode, anode
Voltmeter
Figure 2. A picture of the equipment used.
The mercury lamp emits 6 distinct frequencies of light within the visible range. For the green and yellow bands,
the green and yellow filters are needed (respectively) to ensure that no other higher energy light sneaks in.
First, the lamp has to be warmed up. This takes about five minutes. We then connected the voltmeter to the
detector apparatus. To gather data, we turned the light off (again, to prevent multiple frequencies of light being
incident on the cathode), and positioned the apparatus such that only one color of light was incident on the
detector. We then recorded the stopping voltage as well as the frequency of the incident light, which is known
for mercury, and recorded in Table 1. After every measurement, it is necessary to clear the anode of its residual
charge to get a clear reading. This is done by pressing a button on the side of the detector. Figure 3 explains the
inner workings of the detector.
Color
Yellow
Green
Blue-green (weak)
Blue
Violet
Ultraviolet
Frequency (1014 Hz)
5.18672
5.48996
6.09830
6.87858
7.40858
8.20264
Table 1. Frequencies of light emitted by mercury.
Figure 3 – A diagram of what is happening inside the detector.
Data & Analysis
Because of how little variance there was between the two readings, it was determined that more data was not
going to enhance the accuracy or precision of the experiment, so only two trials were made.
(color)
Frequency
Volts (V)
Yellow
5.19E+14
0.648
Green
5.49E+14
0.778
Blue-green
6.10E+14
1.103
Blue
6.88E+14
1.378
Violet
7.41E+14
1.592
Ultraviolet
8.20E+14
1.905
trial2
Yellow
5.19E+14
0.651
Green
5.49E+14
0.778
Blue-green
6.10E+14
1.109
Blue
6.88E+14
1.382
Violet
7.41E+14
1.592
Ultraviolet
8.20E+14
1.905
Table 2. Frequency of incident light compared with stopping potential (V).
The above data was taken and placed in Graphical analysis, plotting frequency vs. Voltage. The following graph
resulted:
Figure 4. Graph of frequency vs voltage for our data. Gives the slope as 4.146E-15.
Recalling equation (2), the slope should be equal to h/e. Using the accepted values for h and e, h/e should be
4.13567, which is only 0.25% different from the obtained value. The measured value of h was 6.636E-34,
compared to 6.626E-34.
According to the PASCO website, the work function of the photodiode (cathode) is 1.36 +/- 0.08 eV. Our
measured W0 is 1.477 eV, which falls slightly outside that range.
For more details on the exact calculations, see the attached Excel file.
Error Analysis
Because of the cleanness of the data, the only realistic source of error in this experiment is the voltmeter. For
the voltmeter we were using, the Extech MN35, in the range we were using it the error was +/- 0.5%. Using only
this error, the uncertainty in the measured value of h was as follows:
Absolute error
min value h
6.54E-34
1.339%
max value h
6.74E-34
1.742%
Table 3. Using error only from the multi-meter.
However, if one also incorporates the error inherent in the use of linear regression, the uncertainty is somewhat
larger.
Absolute error
min value h
6.30E-34
4.954%
max value h
6.98E-34
5.357%
Table 4. Using error from linear regression.
Regardless of which method for the calculation of uncertainty, the median remains in the same place, at 6.636E34, and both sets of error bounds contain the actual value of Planck’s constant.
The uncertainty for the work function of 1.477 eV was found to be 0.141, which is wide enough that it
incorporates PASCO’s given value of 1.36 +/- 0.08 eV.
Conclusion
This experiment used the photoelectric effect and specific apparatus to determine the value of Planck’s
constant. A mercury lamp was used as the light source, and the energy of ejected electrons was determined by
the stopping potential created by their moving to the anode. The value of Planck’s constant was determined to
be within 0.25% of the accepted value, with a maximum uncertainty of +/- 5%.
We demonstrated that the photoelectric effect is both real and measurable. In order to improve both accuracy
and precision of the lab, using more elements as sources of light would have been useful – it would have given
more data points, and reduced the reliance on a single lamp.