Download Laboratory Exercises in Physics 2

University of Oulu Student Laboratory in Physics
Laboratory Exercises in Physics 2
PHOTOELECTRIC EFFECT
1. Introduction
The photoelectric effect is one of the processes through which the light and the matter
interact. When a metal surface is illuminated with a suitable electromagnetic radiation,
generally with the ultraviolet or the visible light, it emits electrons. The photoelectric
effect was first observed in 1887 when Heinrich Hertz discovered that electrodes
illuminated with the ultraviolet light create sparks more easily. Numerous other
scientists made observations on the photoelectric effect in late 19 th and early 20th
centuries, but these observations could not be understood using classical physics.
In 1905, Albert Einstein published a paper applying Planck’s idea of light quanta to
the photoelectric effect’s experimental data. Einstein explained the observations of the
photoelectric effect assuming that the light energy was carried in discrete quantized
packets. Study of the photoelectric effect was a remarkable stage in the development
of the quantum theory. It helped to understand better the quantum nature of light and
electrons. In 1921, Einstein was awarded the Nobel Prize of physics for his discovery
of the law of the photoelectric effect.
In this laboratory exercise, the theory and the measurements of the photoelectric effect
are studied. The photoelectric effect is examined especially as one proof of the waveparticle dualism and the quantum nature of light. By measuring the stopping potential
as a function of the frequency the Planck’s constant and the work function of the
cathode material used are determined.
2. Studies of the photoelectric effect
2.1 Structure of the measurement apparatus
Fig. 1 shows a typical apparatus used to study the photoelectric effect. The apparatus
includes the following components:
Light source resembles a black body, e.g. it emits radiation in the wide spectral range
also in the regions of visible or ultraviolet light, which are important in the case of the
photoelectric effect. For example a light bulb can be used. In some experiments the
intensity of the light source is adjustable.
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Monochromator is used to choose the desired wavelength from the continuous
spectrum of the light source. The essential device is a rotating grating or a prism,
which directs only one wavelength at a time to an output slit.
Photo cell is a vacuum tube with quartz windows and two electrodes. Quartz is used
as the window material because it is transparent also for the UV light. The cathode (C)
is a plate coated with some suitable material which emits electrons when illuminated
with the light coming from the monochromator. The emitted electrons are called
photoelectrons. The anode (A) can be for instance a platinum spiral.
External current circuit including a tunable power source, an ammeter (AM) and a
voltmeter (VM) connects the electrodes. With the tunable power source the anode’s
potential respect to the cathode can be adjusted in the range (-V, +V). The sensitive
ammeter is capable to measure the small currents called photocurrents flowing in the
circuit and the voltmeter measures the potential difference between the electrodes.
Photo cell
A
Grating
hf
C
Monochromator
AM
Adjustable light source
VM
Tunable power source
Figure 1 An apparatus used to study the photoelectric effect.
2.2 The intensity experiment
In the intensity experiment the photocurrent Iph is measured as a function of the light
source’s intensity I. The wavelength of the light is constant during the measurement.
The anode is held at a sufficiently high potential compared to the cathode so that all
the electrons emitted from the cathode reach the anode. The observed photocurrent Iph
is presented as a function of the intensity I of the light source in Fig. 2.
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Laboratory Exercises in Physics 2
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Iph
I
Figure 2 The photocurrent as a function of the intensity of the light source.
The result of the intensity experiment is not surprising. If the light causes the cathode
material to emit electrons it can be understood that the number of the emitted electrons
is directly proportional to the amount of the light, e.g. the intensity. According to the
classical theory the photoelectric effect can be explained by assuming that the
oscillating electric field of the incident light wave can occasionally knock an electron
out of the cathode’s surface. The more intense light means the greater amplitude of the
electric field, which can release more electrons than the field with the weaker
amplitude.
2.3 The frequency experiment
In the second experiment the intensity of
the light source as well as the potential
difference between the electrodes are
held constant. The photocurrent Iph is
measured as a function of the light
frequency f. The graphs in Fig. 3
represent the results achieved using three
different light source’s intensities
(I 1 > I 2 > I 3 ) .
Iph
I1
I2
I3
f
f0
Figure 3 The photocurrent as a function of the
frequency with different intensities of the light
source.
According to the classical wave theory, the photoelectric effect should be observed at
any frequency of the incident light whose intensity is large enough. The result of the
frequency experiment shows surprisingly that there is a threshold frequency f0
characteristic to the cathode material below which the photoelectric effect does not
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occur no matter how intense the light. With the greater intensity the current increases
more steeply when the frequency is increased, but no current is flowing if the
frequency is below f0.
Based on the classical theory some kind of frequency dependence of the current can be
expected. The electrons inside the matter were thought to move periodically and so the
electromagnetic radiation with a frequency similar to the frequency of the electronic
motion would release more electrons. However, the observed threshold frequency
can’t be explained with this model.
2.4 The potential difference experiment
In the third experiment the photocurrent is measured as a function of the potential
difference VAC between the electrodes. Fig. 4 shows the resulting photocurrent Iph as a
function of the potential difference VAC for a light of constant intensity for three
different frequencies ( f1 > f 2 > f 3 > f 0 ) . Fig. 5 shows the photocurrent as a function
of the potential difference for a light of constant frequency and three different
intensities ( I1 > I 2 > I 3 ). When the potential difference is sufficiently large and
positive all the electrons emitted from the cathode are collected to the anode. So, in the
figures 4 and 5 the curves level off at large positive values of voltage VAC and the
photocurrent obtains a saturation value.
Iph
f1
1
-V0
f2
f3
2
-V0
3
-V0
VAC
Figure 4 The photocurrent for three different light frequencies as a function
of the potential difference between the anode and the cathode.
If the polarity of the power source is reversed, the cathode is at a higher potential than
the anode and the potential difference VAC is negative. Now the electrical force on the
electrons is toward the cathode. If the magnitude | VAC | of the potential difference is
not too great, a part of the electrons can still reach the anode and the photocurrent is
observed. However, when the magnitude of the potential difference is increased, the
current decreases. When the potential difference becomes negative enough the current
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stops. The value V0 of potential difference required to stop all the electrons is called
the stopping potential.
Iph
I3
I2
I1
VAC
-V0
Figure 5 The photocurrent for a constant light frequency for three different
light intensities as a function of the potential difference between the anode
and the cathode.
From the curves in the Fig. 4 we see that the stopping potential V0 increases if the
frequency of the incident light is increased. When examined more precisely it turns
out that the stopping potential is linearly proportional to the frequency. Fig.6 shows
the stopping potential as a function of
V0
the frequency. Using the classical
wave model of the light this
dependence between V0 and f could
not be understood. From the Fig. 5 it
can noticed, that if the intensity of the
light is increased while the frequency
is kept constant, the current levels off
f
at a higher current value, showing that
f0
Figure 6 The stopping potential as a
more electrons are being emitted per
function of the light’s frequency.
time. But the stopping potential V0
remains the same. This can’t be explained on the basis of classical physics. When the
intensity is increased the electrons should gain more energy and so the stopping
potential should increase.
2.5 Einstein’s quantum model
Einstein assumed that the light consists of small energy packets called light quanta or
photons. These photons resemble particles although they don’t have a rest mass. They
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have a momentum and they can collide like any particles. The energy of a photon is
directly proportional to its frequency f so that the proportional constant is Planck’s
constant h, e.g.
hc
E = hf =
,
(1)
l
where c is the velocity of light and l is the wavelength.
The results of the studies considered above can easily be understood with Einstein’s
photon model. A photon arriving to the cathode collides with an electron, which
absorbs the energy of the photon. Greater intensity in the intensity experiment means a
greater number of photons per second absorbed and thus more electrons are emitted
per second and the photocurrent increases.
In the frequency experiment the frequency of the light, e.g. the energy of the photons
arriving to the cathode was decreased until the threshold frequency, below which no
electrons are emitted, was achieved. The electrons at the surface of the cathode are
more loosely bonded than the electrons deeper in the cathode material. The minimum
amount of energy needed to remove an electron from the cathode is called the work
function W . With Einstein’s quantum model the existence of the threshold frequency
f 0 is understandable. The photon with the threshold frequency has just enough energy
for removing the electron from the cathode, e.g.
hf 0 = W .
(2)
The photons with a frequency lower than f 0 do not have enough energy to remove
electrons and no photocurrent is flowing. The work function is characteristic to the
cathode material. Some materials, for example cesium and potassium have so small
work functions, that the quanta of visible light are capable to release electrons from
them.
When a photon collides with an electron of the cathode it gives all its energy to the
electron. If this energy is greater than the work function the electron escapes from the
cathode. Einstein applied the conservation of the energy and stated that the maximum
kinetic energy K max of the emitted electron is the energy hf gained from the photon
minus the work function W, e.g.
K max = hf - W .
(3)
In the potential difference experiment only the electrons having sufficiently high
kinetic energy reach the anode when the polarity of the power source is reversed and
the potential difference VAC becomes negative. When the potential difference between
the electrodes is set to the value - V0 the most energetic electrons leave the cathode
with the kinetic energy K max and arrive to the anode with zero kinetic energy. As the
electron moves from the cathode to the anode, the electric field does the work - eV0
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on the electron. According to the energy conservation law the work done on the
electron is equal to the change in the electron’s kinetic energy and so we get
- eV0 = 0 - K max Þ K max = eV0 ,
(4)
where e is the unit charge. By combining the equations (3) and (4) the photoelectric
law
eV0 = hf - W
(5)
is obtained. From the photoelectric law it can be seen that the stopping potential is
linearly dependent on the frequency according to the equation
W
h
V0 = f - 0 .
(6)
e
e
3. Measurement equipment
The actual measurement equipment used in this study is shown in Fig. 7. The light
source behind the monochromator is a bulb. The monochromator consists of entrance
and output slits as well as of plane and spherical mirrors and two reflecting gratings
enclosed in a box. The gratings are placed onto the same axis so that by rotating the
axis with a selector either one of the gratings can be chosen. In this study the grating
operating in the visible region is used. On the side of the box there is a crank. By
turning the crank the chosen grating rotates and only one wavelength at a time is
directed to the output slit. The wavelength of the monochromatic light in nanometers
can be seen from the scale on the top of the box.
The photo cell is placed inside a metallic casing, which has a slit for the light coming
from the monochromator. The cell includes a cathode plate coated with potassium and
a platinum spiral anode.
The measurements of this exercise resemble the potential difference experiment
discussed above. The photocurrents are measured as a function of the potential
difference between the anode and the cathode. The external current circuit includes a
power source connected to a potentiometer for tuning the potential difference between
the electrodes, a voltmeter for measuring the potential differences and a very sensitive
ammeter for measuring the small photocurrents. In this study the polarity of the
power source is reversed compared to that shown in the Fig. 1, e.g. the voltage VAC is
negative throughout the measurements.
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Grating selector
Crank
Potentiometer
Monochromator
Ammeter
Power source
Voltmeter
Photo cell
Figure 7 The measurement equipment.
4. Exercises
Answer the following questions before coming to the laboratory:
1. Explain shortly what is measured in the a) frequency and b) potential difference
experiment. What kind of observations in these experiments could not be
explained using the classical physics?
2. What kind of explanations to the observations mentioned above gave Einstein’s
quantum model?
3. Why must the measurement equipment include the monochromator? How does the
monochromator work?
5. Measurements and analysis
5.1 Measurements
1. Preparations: Check the circuit with the tutor. Turn the light bulb on. Prepare the
Valokenno
monochromator for the measurements with the tutor. First, check that the grating
operating at the visible region is chosen. Then choose the first wavelength (around
400 nm) by rotating the grating with the crank to the right position. Check that the
potentiometer is set to zero value and turn the power source on. Then turn also the
ammeter and the voltmeter on and check on the basis of the current and the
voltage readings that the light hits well to the photo cell. Set the potential
difference first to the value around -1.5 V.
Monokromaattori
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Laboratory Exercises in Physics 2
2. Measuring the photocurrents: Choose five wavelengths in the range 360-520 nm
to be used in the measurements and measure the (VAC, Iph)-curves with each
wavelength by tuning the potential difference from the starting value to zero in
suitable steps and register the corresponding photocurrents. When the photo cell
has been used a small amount of potassium has drifted to the anode. During the
measurement the light can thus release electrons also from the anode. This causes
that with the first, quite large negative values of the potential difference VAC a
small photocurrent is flowing from the anode to the cathode. So, the first currents
observed are negative. The actual (VAC, Iph)-curves observed in this study thus
resemble the curve shown in Fig. 8.
Iph
From the Fig. 8 it can be seen that
= measurement points
different tuning steps of the voltage
with 30 mV steps
should be used in the measurements.
= measurement points
When the potential difference’s
with 100 mV steps
magnitude is large and the
photocurrent is negative the currents
can be register in 100 mV steps. The
VAC
-V0
most interesting part of the curve is
the region where the current is near
Figure 8 An example (not to scale)
zero. So, in this region a smaller
of an observed (VAC, Iph)-curve.
tuning step around 30 mV can be
used. When the current has changed
positive and begins to increase more steeply 100 mV is again a suitable tuning
step.
Because the photocurrents are very small the measurement equipment is
extremely sensitive especially to various electrical perturbations. For example the
charges on the clothes can disturb the measurement. Therefore, the clothes made
of easily electric synthetic fibres should be avoided. It is also recommended to
move as few as possible during the measurements in order to avoid the generation
of the static electricity. The amount of the background light should be kept same
throughout the measurements.
5.2 Analysis
1. The (V AC , I ph ) -graphs and determining the stopping potentials: Present the
observed photocurrents in the (V AC , I ph ) -coordinate system and draw a curve
representing the photocurrent as a function of the potential difference after the
measured points with every wavelength used.
Determine the corresponding
stopping potentials from the curves.
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2. Determining the Planck’s constant and the work function: Change the used
wavelength values to the frequencies and show the determined stopping potentials
as a function of the frequency in the ( f ,V0 ) - coordinate system. Fit the straight
line represented with the Eq. (6) to these ( f , V0 ) -points by using the least squares
method. Determine the slope and the intercept of the line with their error limits
and calculate the Planck’s constant (in units Js) and the work function (in units
eV) with their absolute and relative error limits. Compare the results with the
values given in the literature.
3. Considering the possible influence of the thermionic emission: The electrons on
the surface of the cathode create a so called electron gas where electrons can move
almost freely in the cathode material. The electrons can escape from the cathode’s
surface as a result of the thermionic emission which is caused by heating the
material so that the kinetic energies of the electrons increase sufficiently high. Has
the thermionic emission any influence to the results of this study? Give also the
reasons to your answer.
(Hint: The kinetic energies of the electrons are
distributed according to Maxwell-Boltzmann distribution.)
Remember to attach the answers of the exercises and to the thermionic emission
question above as well as the (V AC , I ph ) - and the ( f ,V0 ) - graphs to your report.
UNIVERSITY OF OULU
Student: ___________________________
STUDENT LABORATORY IN PHYSICS
Date of measurements: ____ / ____ 20___
Laboratory Exercises in Physics 2
Tutor: _____________________________
MEASUREMENT FORM
PHOTOELECTRIC EFFECT
l=nm
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l=nm
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l= nm
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Tutor’s signature _________________________________
l=nm
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