19 Jul 11
Planck.1
THE PHOTOELECTRIC EFFECT
In this experiment you will study the emission of electrons from a metal surface that is
illuminated with light of various discrete frequencies. You will measure the dependence of the
kinetic energy of the emitted electrons on the frequency of the incident light and you will
examine the effect of varying the intensity of the incident light.
Theory: The Photoelectric Effect
Late in the nineteenth century a series of experiments revealed that electrons are emitted from a
metal surface when it is illuminated with light of sufficiently high frequency. This phenomenon
is known as the photoelectric effect.
In 1905, Einstein explained the photoelectric effect by assuming that light propagates as
individual packets of energy called quanta or photons. This was an extension of the quantum
theory developed by Max Planck. In order to explain the spectrum of radiation emitted by
bodies hot enough to be luminous, Planck assumed that the radiation is emitted discontinuously
as bursts of energy called quanta. Planck found that the quanta associated with a particular
frequency  of light all have the same energy, E = h, where h = 6.626 × 10–34 J·s
= 4.136 × 10–15 eV·s (Planck’s constant). Although he had to assume that the electromagnetic
energy radiated by a hot object emerges intermittently, Planck did not doubt that it propagated
continuously through space as electromagnetic waves. Einstein, in his explanation of the
photoelectric effect, proposed that light not only is emitted a quantum at a time, but also
propagates as individual quanta.
Einstein’s explanation of the photoelectric effect is that it is a result of collisions between
photons (light quanta) of the incident light beam and electrons in the metal surface. In the
collision, the photon energy h is absorbed by the electron. Some of this energy is then used to
overcome the binding energy of the electron to the metal, and the remainder appears as kinetic
energy of the freed electron. This quantum theory of light is totally contrary to the wave theory,
which predicts that light energy is distributed continuously throughout the wave pattern, and
which provides the sole means of explaining many optical effects such as diffraction and
interference. This wave-particle duality cannot be avoided; both theories are required to account
for the observed behaviour of electromagnetic radiation. The ‘true’ nature of light cannot be
described in terms of everyday experience, and both wave and quantum theories must be
accepted, contradictions included, as being closest to a complete description of light.
Apparatus:
The equipment consists of a source of photons (high-intensity mercury vapour light source), a
monochromator (a diffraction grating and a set of interference filters), an intensity filter, a
phototube, an electrometer (essentially a very sensitive ammeter), a DC voltage source in
combination with a rheostat used as a voltage divider, and an interface device which allows
phototube current and retarding potential to be processed by a computer.
The diffraction grating and interference filters enable separation of the light from the mercury
source into prominent spectral lines of discrete wavelength (and hence frequency), the phototube
19 Jul 11
Planck.2
contains the metal surface to be illuminated, and the rest of the equipment is used to measure the
current due to the emitted photoelectrons as a function of retarding potential.
The phototube consists of two electrodes enclosed in an evacuated tube. One electrode (the
cathode) has a large photosensitive surface and is called the emitter. The other electrode (the
anode) is a wire and is called the collector. When the emitter is exposed to light, electrons are
ejected from its surface. Some of the emitted electrons strike the anode, causing a current to
flow. This current is measured by the electrometer. To measure the maximum kinetic energy,
KEmax, of these emitted electrons, a retarding potential is applied across the cathode and anode.
The anode is made progressively more negative than the cathode, resulting in fewer and fewer
electrons having sufficient kinetic energy to overcome this retarding potential difference. When
the anode potential becomes sufficiently large (equalling Vo, the stopping potential), subsequent
photoelectrons have insufficient kinetic energy to overcome the potential difference, so no more
electrons reach the anode and the phototube current reaches zero. This occurs when KEmax =
eVo. A value of Vo is determined by analysing the plot of phototube current versus retarding
potential obtained from the computer.
Determining Vo for various known discrete frequencies of light allows analysis of the
relationship between KEmax and 
The intensity filter is used to determine if Vo (and hence KEmax) depend on the intensity of the
incident light.
Procedure and Experiment:
NOTE:
For best results, this experiment should be done with the room lights off. Also, avoid
bumping the equipment as proper alignment is crucial.
Turn on the mercury light source, the electrometer, the DC voltage source, the digital voltmeter,
and the computer interface.
Ask the instructor to explain the operation of the equipment and DataStudio software.
The spectral lines to be measured are:
violet
violet
blue
green
yellow
365.0 nm
404.7 nm
435.8 nm
546.1 nm
578.0 nm (ave. of 577.0 nm and 579.1 nm)
Filters are available for all but the 365.0 nm line. Using the provided holder the desired filter
should be positioned as close as possible to the aperture of the mercury light source.
For each of the first order spectral lines, acquire phototube current versus retarding potential
data.
19 Jul 11
Planck.3
For the first order green line, acquire phototube current versus retarding potential data for each of
the intensities provided by the intensity filter.
Analysis:
Use the DataStudio software to determine the stopping potential for each of your sets of data of
phototube current versus retarding potential. Determine the stopping potential as accurately as
possible and be sure to record a reasonable uncertainty in your values.
Plot maximum photoelectron energy (KEmax = eVo) versus light frequency, . Remember to
calculate and include error bars for the energy values.
Applying conservation of energy to the photon-electron interaction described by Einstein yields:
Ephoton = Eelectron
Ephoton = KEelectron + BEelectron
where KEelectron is the kinetic energy of the emitted electron and BEelectron is the energy required
to overcome the binding energy of the electron to the metal.
The work function,, is the minimum energy required to remove an electron from the metal
surface being illuminated. Electrons that have this minimum binding energy will therefore have
the maximum kinetic energy upon release.
Thus
and since
Ephoton = KEmax + 
Ephoton = h ,
hKEmax + 
which can be written as
KEmax = h – 
Does your graph of maximum photoelectron energy versus light frequency agree with this
equation (Einstein’s equation of the photoelectric effect)?
Draw the best-fit line and the maximum-fit line through your data. Assuming the Einstein
equation is correct, determine values for h, Planck's constant, and, the work function, from your
graph. Compare your value of h (and its error range) with the accepted value of
6.626 × 10–34 J·s or 4.136 × 10–15 eV·s.
Based on your data acquired using the intensity filters, does KEmax depend on the intensity of the
incident light? Does any parameter of the photoelectric effect depend on the intensity of the
incident light? Interpret your answers to these questions in terms of Einstein’s explanation of the
photoelectric effect.
19 Jul 11
Planck.4
Detailed Description of Equipment and Procedure
Light Source
The source of light is a mercury discharge lamp. Light from the lamp is passed through an
interference filter to select the desired wavelength. The light is then passed through a diffraction
grating to further ensure that only the desired wavelength is illuminating the phototube. A
neutral density filter is available to vary the intensity of the incident light without affecting the
wavelength.
mercury
discharge
lamp
diffraction
grating
interference
filter
Phototube
The phototube is housed in a light-tight container with an entrance port for the incident light. A
mask on the entrance port reduces the exposure of the collector to the incident light. (Light
incident on the collector causes a “reverse” current of opposite polarity to the current due to the
photoelectrons that are being studied.) Electrical connections to the phototube allow the
application of a voltage across the emitter and collector and allow measurement of the electric
current flowing between the emitter and collector.
19 Jul 11
Planck.5
entrance port
entrance mask
electrical connections for
measuring current and
voltage
Power Supply and Voltage Divider
The Electro Industries Power Supply is set for the 0-15 V range, with the current control set at
maximum. The output of the power supply is connected across an 85  rheostat which is being
used as a voltage divider. The slider of the rheostat is set so that the voltage available across the
rheostat slider and ground connections varies from 0 to 3 volts as the power supply voltage is
varied from 0 to 15 volts. The rheostat slider and ground connections are used to apply the
retarding potential to the phototube and are also connected to the Channel A Analog input of the
Science Workshop 750 Interface.
rheostat used as
voltage divider
voltmeter to monitor
retarding potential
power supply for
retarding potential
19 Jul 11
Planck.6
Keithley 616 Digital Electrometer
The lead from the phototube that allows measurement of the emitter-collector current is
connected to the input of the electrometer. The electrometer is set for “FAST” response,
midrange sensitivity, and 10–6 A. The 0-1 V output available at the back of the electrometer is
connected to the Channel A Analog input of the Science Workshop 750 Interface.
Science Workshop 750 Interface
The Science Workshop interface connects to a PC via a standard USB cable and allows the data
to be collected, processed, and saved using the DataStudio software loaded on the PC. The
Channel A Analog input of the interface receives the retarding potential data via a CI-6503
voltage sensor. The Channel B Analog input of the interface receives the phototube current data
also via a CI-6503 voltage sensor.
19 Jul 11
Planck.7
Schematic Diagram of Component Connections
DataStudio Software
As mentioned, the DataStudio software enables the experiment to be run via a PC.
To prepare the interface:
1. Double-click the DataStudio icon on the PC desktop
2. Click “Create Experiment”
3. Click the CH A port on the display of the Interface, select Voltage Sensor, and click OK.
4. Set Sample Rate to 200 Hz and select Low (1)
5. Click the CH B port on the display, select Voltage Sensor, and click OK.
6. The Sample Rate should show 200 Hz. Select Med (10)
The data acquisition system is now ready for use.
Detailed Procedure
To acquire data:
1. Arrange the light source, diffraction grating, and filter so that the desired spectral line is
focussed and centred on the entrance port of the phototube holder.
2. If necessary, switch off the “ZERO CHECK” on the electrometer.
3. Click the “Start” button in the DataStudio software, and slowly and steadily increase the
retarding potential by turning the voltage control on the Electro Industries power supply.
4. When the applied retarding potential reaches 3 V click “Stop” in DataStudio.
19 Jul 11
Planck.8
Detailed Data Analysis
Under “Displays” in the left-hand column of DataStudio double-click Graph, select Run #1
under Voltage CH B as the source, and click OK.
The graph shows the electrometer output (proportional to phototube current) as a function of
elapsed time.
To obtain the desired graph of electrometer output versus retarding potential, in the “Data”
section of the left-hand column of DataStudio click Run #1 under Voltage CH A and drag to the
x-axis of the graph.
The graph of electrometer output versus retarding potential should show a rapid and steady
decrease followed by a long tail where the electrometer output is constant (see sample graph
below).
The stopping potential (the retarding potential required to just stop all of the emitted electrons
from reaching the collector electrode) is the voltage at the start of the constant electrometer
output tail. Alternatively, starting from high values of retarding potential and looking toward
lower values, the stopping potential is the value of retarding potential at which the electrometer
output starts to increase from the current value of the tail.
Phototube Current vs. Retarding Potential for Hg Green Line approximate stopping potential 19 Jul 11
Planck.9
Choosing appropriate scales allows accurate determination of the stopping potential:
stopping potential
The data can either be analysed within DataStudio or saved to a file for later analysis using a
spreadsheet program such as Microsoft Excel.
To analyse the data within DataStudio, note that the graph can be easily manipulated:

clicking and dragging the plot area near either of the axes allows adjustment of the
starting values on the graph axes;

clicking and dragging the numbers on each of the axes allows the axes scales to be
adjusted independently.
To save the data as a tab-delimited text file, click File, Export Data…, select Run #1 under
Voltage CH B vs Voltage CH A, and click OK.
Choose an appropriate location for the data file, give it a descriptive filename, and click Save.
The data file can be opened in Excel for graphing and analysis at a later time.