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The Photoelectric Effect
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1. Objective
Students will be introduced to the photoelectric effect and two competing theoretical
explanations of the effect. In a series of measurements they will differentiate between the two
theoretical explanations and determine which best agrees with their observations.
2. Introduction
Discovery
In 1899, J.J. Thomson discovered that when a metal target is irradiated by ultraviolet light it
emits negative charges. These charges were found to have the same charge/mass ratio as the
electron. This effect was named the photoelectric effect, and the emitted electrons called
photoelectrons. To explain the effect, a mechanism was proposed by which the energy in the
oscillating electric field of the UV light was continuously transferred to the bound electrons.
Electrons that had absorbed more than a certain amount of energy characteristic of the metal Eo ,
(called the work function), would be discharged with a kinetic energy (Ek) equal to the difference
between the total energy absorbed by the electron (Ee) and the work function (Eo ):
Ek = Ee - Eo
(1)
This explanation was based on Maxwell’s very successful theory of light. In Maxwell’s theory
the energy present in electromagnetic fields is distributed continuously throughout the spatial
extent of the field and is proportional to intensity of the field (the square of the field). One
corollary of this explanation was that if metal was irradiated by very dim light, it would take a
while for the electrons to absorb energy equal to Eo and therefore the discharge would be delayed
slightly.
First study
Shortly after the discovery of this effect Philip Lenard performed the first systematic study of the
photoelectric effect. He used a glass vacuum chamber with two electrodes configured as an
anode and cathode, and a window to allow light to shine on the cathode surface. By using an
ammeter Lenard was able to measure the photocurrent as a function of the intensity and
frequency of the light. By varying the potential difference (ΔV) between cathode and anode
Lenard could measure the kinetic energy of the photoelectrons ejected from the cathode. Lenard
made a number of observations which appeared to be at odds with the originally proposed
explanation.
1) Current is proportional to the intensity of the irradiating light.
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2) Current appears without delay regardless of the dimness of the irradiating light source.
3) Photoelectrons are emitted only if the frequency of the irradiating light source exceeds a
threshold frequency f o . The value of f o appears to be characteristic of the type of cathode
metal.
4) If the potential difference ΔV is made negative (electrons are decelerated as they
approach the anode) the current decreases until it becomes zero (at ΔV=Vstop ). Vstop is
called the stopping potential and it is independent of the intensity of the irradiating light
source but dependent on the frequency of the source. An electron with kinetic energy Ek
ejected by the cathode will be prevented from reaching the anode by a stopping voltage
Vstop = Ek / e
(2)
Einstein’s interpretation
In his famous 1905 paper Einstein noted that
“The usual conception that the energy of light is continuously distributed over the space through
which it propagates encounters very serious difficulties when one attempts to explain the
photoelectric effect…”
To explain the observations made by Lenard, Einstein argued that the energy associated with the
electromagnetic field was not continuous; it didn’t just “flow into” the electrons at a rate
proportional to the intensity. Instead, he postulated that it possessed a sort of granularity, arriving
in packets of size
E=hf,
(3)
where h = 6.63×10-34 J⋅s is Planck’s constant and f is the frequency of light. In the presence of
quantized electromagnetic radiation an electron can escape from a metal if hf ≥ Eo where any
excess energy becomes the kinetic energy of the ejected electron. If we assume the intensity of
the light is not high enough for electrons to have a very high chance of absorbing more than a
single photon then we can combine (1), (2), and (3) to obtain Einstein’s equation for the
photoelectric effect:
eVstop = hf - Eo
(4)
Vstop = (h/e)[f - f o ]
(5)
Or in terms of frequency:
It is clear from equation (5) that a graph of Vstop vs f provides a way to measure Planck’s constant
h and the cutoff (or threshold) frequency f o .
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3. Equipment
The light source used in the apparatus consists of several interchangeable light emitting diodes
(LEDs). Figure 2 shows the experimental arrangement.
The LEDs should be mounted on the power supply box so that light enters the phototube and is
incident on the cathode. There are 8 diodes emitting from 390 nm (UV) to 934 nm (IR), a
variable intensity LED and an oscillator driven LED. Some spectral widths are given below.
Color
Blue
Cyan
Green
Amber
Orange Red
Red
Infrared
λ (nm)
390
455
505
535
590
615
640
935
Δλ (nm)
40
40
30
30
10
10
10
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The experiment is performed using each LED as a monochromatic light source. Ejected electrons
impinging on the anode creates a current which is converted to a voltage across a 100-kΩ
resistor. The main controller box has a bnc-connector for the phototube, a built in potentiometer,
and ports for multimeters to measure the voltage output by the potentiometer and the voltage
generated by the photocurrent. The experimental setup is equipped so that you can repeat
Lenard’s famous experiments.
1) Using the built-in potentiometer, the photocurrent can be adjusted to zero and thus the
stopping voltage can be measured (see equation 2).
2) Using the variable intensity LED both the photocurrent and stopping voltage can be
measured as a function of the intensity of the irradiating source.
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3) Using a function generator to generate a square wave, the oscillator-driven LED, and
an oscilloscope the delay between incident light and photocurrent response can be
studied.
4. Instructor’s expectations
During the lab session students
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assemble the apparatus;
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make a sketch, or a photo, or use any available source to present the working setup in the
lab report with main parts of the apparatus linked to the drawing in Fig. 2;
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perform exercises detailed in section 6;
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fill out a lab report including some theoretical background/introduction, a description of
the exercises carried out, the results of the exercises, analysis of the sources of
uncertainty, detailed responses to all questions in the exercises, and give a summary of
the experiment and findings.
The lab report must be not exceed 6 pages of an electronic document in the format PDF or Word,
or any other format that permits commenting by an Instructor right in the text. The report
submission is expected not later than in 6 days after the lab session.
5. The experiment
Exercise 1) Insert a LED into the power supply socket and turn it on. Align the diode head with
the phototube window. Set up the two multimeters as voltmeters (remember that photocurrent is
measured as a potential drop across the 100-kΩ resistor). With the potentiometer on, measure the
stopping voltage (Vstop ) for each of the 8 wavelengths provided. Adjusting the photocurrent to
zero will require the most sensitive range on the multimeter. Estimate/calculate errors and graph
the stopping voltage vs. the frequency of the light. Determine the following quantities:
1) Planck’s constant h,
2) the work function Eo ,
3) the cutoff (threshold) frequency f o .
Exercise 2) Use the variable intensity LED and independently measure the stopping voltage and
the photocurrent as a function of intensity. Graph Vstop and the photocurrent vs. the intensity
setting. Intensity units are arbitrary. Comment on the results in light of the original explanation
of the photoelectric effect and Einstein’s explanation.
Exercise 3) Connect the phototube to Ch1 of the oscilloscope through the rectifying adaptor. DO
NOT TURN ON THE PHOTOTUBE POWER SUPPLY. Connect the wave generator to the
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oscillator-driven LED and also to CH2 of the oscilloscope. Turn on the function generator and
adjust the output to get a square wave with a frequency on the order of 1-2 kHz. Set the
oscilloscope to trigger off Ch2 and adjust the settings to get 1-4 full periods of oscillation within
the viewing window. If needed, use Acquire → Average functions and a 20MHz filter. Measure
the transient photocurrent as a function of time and estimate the delay between incident light and
a response in the photocurrent.
The electric power consumed by the oscillator-driven LED is 60mW. Assume all this power is
converted into light (PLED). The photocathode area is APC = 3.23cm2 . Each electron receives a
fraction of the power Pe given by:
Pe = PLED (Ae/APC).
(6)
Knowing that in solids electrons are ~.3nm away from each other, calculate the energy absorbed
by each electron in a second. Using the work function that you determined in Exercise 1,
estimate the time that an electron will need to absorb enough energy to escape the photocathode.
Compare this with the measured time delay between incident light and a photocurrent response
and comment on the result in light of the original explanation of the photoelectric effect and
Einstein’s explanation.
References and recommended readings
1. R. A. Serway , J. W. Jewett: Physics for Scientists and Engineers, 9th Edition. Chapter 40.
2. Randy Harris: Modern Physics. Second Edition.
3. W. P. Garver: The Photoelectric effect Using LEDs as Light Sources, The Physics Teacher 44
(p.272-275), 2006.
4. 4. Einstein’s Proposal of the Photon Concept-a Translation of the Annalen der Physik Paper of
1905*.A. B. Arons and M. B. Peppard. Am. J. Phys.33,5(1965).
This guide sheet was written in 2016 by Josiah J. Sinclair.