Download Photoelectric Effect

Photoelectric Effect
Equipment
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Leybold Photocell
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Jarrell Ash Monochromator
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Cary vibrating reed electrometer
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Tungsten-Halogen lamp
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Metrologic He-Ne laser
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Fluke multimeter
precision voltage divider
10 V DC power supply
flashlight
nanoAmpere current source
1 m optical bench
Preparation
You should review Einstein’s explanation of the photoelectric effect.
Review the band theory of conduction in metals, and the diffraction of
light.
Goals of the Experiment
To investigate some properties of the photoelectric effect and photocells. To get some experience with low level current measurements.
To better understand optical spectra by using a monochromator and a
Tungsten-Halogen lamp as a line source.
Theory
The photoelectric effect is one example of an interaction between
energy and matter. In the photoelectric effect, a material is illuminated with a beam of light and electrons are ejected from the material.
These emitted electrons are called photoelectrons. This effect occurs
in any material, whether solid, liquid, or gas. The photoelectric effect
was first noticed by Heinrich Hertz (1857-1894) in 1887 when he observed that shining ultraviolet light into the region between a spark
gap raised the conductivity of the air in the gap. Later experiments
showed that shining ultraviolet light onto a metallic plate gave it a
Figure 13.1: Equipment setup
positive charge. In 1898 Philipp Lenard (1862-1947) and J. J. Thompson (1856-1940) showed that the particles being emitted were actually
electrons. Lenard later won the 1905 Nobel prize in physics for his
work on electrons. Thompson won the 1906 Nobel prize for his related work on the conduction of gases. As described below, the photoelectric effect has many properties that simply cannot be accounted
for by a wave theory of light. In 1900, to partly explain the effect,
Max Planck (1858-1947) suggested that an atom could only absorb or
emit energy in discrete bundles called quanta. He was later honoured
with the 1918 Nobel prize for this insight. It was left to Albert Einstein (1879-1955) in 1905 to fully explain the photoelectric effect using
Planck’s ideas. Einstein’s theory of the photoelectric effect explains all
the observed properties of the photoelectric effect. He won the 1921
Nobel prize for this work. Einstein’s theory of photoelectricity was
experimentally verified by Robert Millikan (1868-1953) in 1916 in a series of careful measurements that also accurately determined Planck’s
constant for the first time. This work earned Millikan a Nobel prize
in 1923. The physics experiment to be done here is in fact similar in
method and construction to Millikan’s prize winning experiment.
If one assumes that the photoelectric interaction is simply a light
wave phenomenon then several conclusions follow immediately. The
wave theory predicts that the energy of the emitted electrons is proportional to the square of the light frequency. Also, there should be photoelectrons at any wavelength, if the light is intense enough. Third, the
electron energy should be proportional to the light intensity. Fourth,
the electrons should be emitted with a large delay that depends on the
light intensity and the illumination area. Lastly, the amount of electrons knocked off should be proportional to the size of the atom and
hence to the amount of surface exposed to the light.
Experimental measurements of the photoelectric effect show that
none of these properties are true. The energy of the photoelectrons
varies linearly with frequency. Below a critical frequency, no photoelectrons are emitted regardless of the light intensity. Furthermore,
the photelectron energy is independent of the light intensity and the
illumination area. Lastly, there is essentially no delay between the arrival of light and the emission of photoelectrons, regardless of the light
intensity and illumination area.
Einstein explained the photoelectric effect by supposing that the energy of electromagnetic radiation is carried in discrete bundles called
photons. The energy, E, of a photon is given by
E = hf
(13.1)
where f is the frequency of the light and h is Planck’s constant.
The currently accepted value for Planck’s constant is 6.6261 × 10−34
2
J · s. Equation 13.1 implies that higher frequency light like ultraviolet
radiation is more energetic than lower frequency light such as infrared
light. Each photon can only give up a discrete amount of energy, E,
to an electron. Suppose that the electron is bound to the material with
energy W. This is then the amount of energy needed to liberate an
electron from the surface of a material. W is called the work function
of the material. Any extra energy is transformed into kinetic energy of
the photoelectron.
The energy balance equation for the incoming photon versus the
outgoing photoelectron is
hf = W + K
(13.2)
where K is the kinetic energy of the photoelectron. Therefore, a
photoelectron has kinetic energy given by
K = hf −W
(13.3)
This equation handily explains all the observed features of the photoelectric effect. There is a lower limit below which the light generates
no photoelectrons because a photon with energy less than W does not
have enough energy to liberate an electron from the surface of the
material. If the photon does have sufficient energy (high enough frequency), an electron is knocked loose as soon as a photon interacts
with it. This explains why the emission of photoelectrons is nearly
simultaneous with the arrival of the illuminating light. Also, Equation
13.3 shows directly why the energy of a photoelectron varies linearly
with the illuminating light frequency. Lastly, Equation 13.3 shows that
the energy of a photoelectron is independent of light intensity. When
a bright light illuminates a surface, many more electrons are knocked
out of the surface because there are more photons, but each photoelectron has the kinetic energy specified by Equation 13.3. Brighter
illumination induces a higher photocurrent, simply because more photoelectrons are in motion.
The arrangement used for examining the photoelectric effect is shown
in Figure 13.2. Light is made to shine on a potassium surface called
the photocathode. Photoelectrons are ejected from this surface and
collected by the nearby platinum ring called the anode. The work
function of potassium is 2.30 eV and the work function of platinum
is 5.65 eV. This means light with a wavelength longer than about 540
nm will not eject electrons from either the platinum or the potassium.
Light with a wavelength shorter than 220 nm will begin to eject photoelectrons from the anode as well as the photocathode. This gives a
window from 540 nm to 220 nm in which photoelectrons are ejected
from the photocathode alone. This is the wavelength range for which
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Equation 13.3 can be examined. The anode and photocathode are in
vacuum so the photoelectrons do not lose energy except at the anode.
Potassium
Photocathode
Photoelectrons
Figure 13.2: Photocell
Platinum Anode
Evacuated
Glass Bulb
Light
A
Adjustable
Stopping
Potential
V
Cary Electrometer
The emission of electrons from the photocathode (photocurrent) is detected by the electrometer. An electrometer is basically an extremely
sensitive current meter. The anode voltage polarity opposes the arrival
of photoelectrons. The energy of the photoelectrons is found by raising the anode voltage to the point where the photocurrent stops. If
the illuminating light is monochromatic, this stopping potential , Vs ,
gives a determination for the kinetic energy of the photoelectrons so
that
h
W
f−
(13.4)
e
e
Since e = 1.6022 × 10−19 C, plotting stopping voltage versus illumination frequency gives a value for Planck’s constant from the slope
of the line. The arrangement of Figure 1 also permits experimental
verification that stopping voltage (kinetic energy) is independent of
light intensity but the photocurrent (as measured by the electrometer)
is strongly dependent on the light intensity. It is also possible to verify
that below a certain critical frequency, no photocurrent is stimulated
regardless of light level.
Equation 13.3 suggests that the intercept of the graph yields the
work function of the potassium photocathode, Wc. A more careful examination indicates that this is incorrect. Both the cathode and the anode are made from metals. This means the outer shell electrons inside
the metal partially fill an energy band called the conduction band. The
highest energy level in the conduction band with an electron in it is
called the Fermi energy. At absolute zero there are no electrons above
the Fermi energy and all energy levels below the Fermi energy are
completely filled with electrons. At higher temperatures this boundary is not sharp as many electrons move to higher levels on thermal
Vs =
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energy alone. The fact the the Fermi energy lies in the middle of the
conduction band explains why the metal is a good conductor. There
are many nearby unfilled energy levels available for the electrons to
occupy.
To fully remove an electron, a surface needs more energy than just
the Fermi energy. The aggregate attraction of the complete metallic
lattice prevents the electron from being free even when removed from
the conduction band. The extra required energy to completely free an
electron from the surface is called the surface barrier energy. The surface barrier energy depends greatly on the exact nature of the surface.
Impurities, trace gases, and crystal structure all affect the surface barrier energy and hence the perceived work function of the material. The
work function for a metal is the sum of the Fermi energy and the surface barrier energy. Figure 13.3 shows an energy level diagram for the
conduction electrons in the metallic cathode and anode. The retarding
voltage applied to the anode determines the potential difference between the Fermi levels in the anode and photocathode. As shown in
Figure 13.3, this is not the retarding potential seen by a photoelectron
travelling between cathode and anode.
To find the true retarding potential as seen by a photoelectron, let
0
Vs be the true stopping potential and Vs be the potential as seen by the
voltmeter. Then from Figure 13.3
Vs0 = Vs +
Wa
Wc
−
e
e
(13.5)
and Equation 13.4 is really
Vs0 =
Wc
h
f−
e
e
(13.6)
As seen by the voltmeter this is
Vs =
h
Wa
f−
e
e
(13.7)
The above discussion suggests that the measured intercept should
be regarded with some suspicion. However, the slope determination is
not affected. It also suggests that the transition of the photocurrent to
zero as the stopping potential is increased will be gradual rather than
abrupt because the photoelectrons arise from a population of conduction electrons with widely varying energies. Some electrons will manage to cross from cathode to anode on thermal energy alone. This is
thermionic emission. Since this current flows even without light, it is
also called dark current. At room temperature the dark current is very
small.
Another obscuring phenomenon is that over time the anode ring becomes contaminated with cathode material. Now the anode will also
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3
4
Wa
eVs0
5
2
Wc
eVs
Anode Fermi Level
1
0
Cathode Fermi Level
Figure 13.3: Energy Levels
0) Photon Arrives
1) Photoelectron overcomes
cathode Fermi energy
2) Photoelectron overcomes
cathode surface barrier
3) Photoelectron overcomes
stopping potential V’
4) Photoelectron attracted by
surface potential
5) Electron moves into the
conduction band
emit photoelectrons when illuminated. This is rectified by heating the
anode until it begins to glow light red. Both ends of the anode are connected to an Anatek power supply capable of delivering 2 Amperes.
Note that under normal operation one side of the anode is left unconnected. The procedure should be done in a darkened room while
carefully observing the anode. The entire process does not last longer
than 15 seconds. This procedure can only be carried out by qualified
lab staff.
Input White Light
(Hot Tungsten-Halogen)
Figure 13.4: Light path of the
monochromator
50 micron Entrance Slit
45 degree mirror
Tiltable reflection grating
45 degree mirror
Main parabolic mirror
50 micron exit slit
Output monochromatic light
The photocell must be illuminated with monochromatic light for
meaningful results. The method chosen for generating such light in
this experiment is called a monochromator. It has the advantage that
a large number of frequencies can be easily generated. This permits a
careful examination of Equation 13.7. The light path of the monochromator is shown in Figure 13.4. In effect, it is a reflection grating spectrometer that is connected backwards. It generates monochromatic
light from a source instead of analyzing one frequency of light from
a source as a spectrometer would. The source used is an ordinary
Tungsten-Halogen lamp. This lamp generates light from the far infrared into the ultraviolet. To select a given wavelength, a knob ro6
tates the grating. Special gears couple this rotation to a display that
reads out the wavelength chosen in nanometers. The output from
the monochromator is not truly monochromatic. The output spectral
width is roughly 1 nanometer.
The photocurrents to be measured in this experiment are on the
order of picoamperes (10−12 Amperes). At these low current levels,
special precautions must be taken to obtain valid measurements. Materials that are normally considered to be insulators become conductors instead. The reason is because a source of picoampere current
at one volt potential has an effective resistance of 1012 Ω. This resistance is comparable to the resistance of many common insulators such
as paper, rubber, and plastic. Instead of insulating the circuit, these
materials act like ordinary resistors and become part of the circuit.
To help with low current measurements, the wiring should be as
short a possible. This minimizes the amount of insulator present and
reduces the area available for noise pickup. The electrometer is designed with this in mind. The sensing preamplifier head is separate
from the rest of the instrument. In this way the sensing head can be
placed very close to the source to be measured using short cables. The
photocell cathode is directly connected to the electrometer sensor head
with a short 20 cm cable.
Materials under mechanical motion or stress exhibit charge imbalances that manifest themselves as currents. These are called piezoelectric effects. Frictional effects such as when two materials rub against
each other also produce charge displacements. These are called triboelectric effects. To eliminate these sources of error, motion, vibration,
and mechanical stress must be prevented in all components, connections, and wiring.
Very high resistance materials like sapphire, quartz, and Teflon should
be used where possible. These have volumetric resistances on the order
of 1017 Ω. The electrometer head is insulated with sapphire. However,
cleanliness is important. Contaminants such as dust, moisture, grease,
fingerprints, and salt provide paths for surface leakage currents. Do
not touch circuit components or wires by hand. Use a tissue or rubber
gloves instead.
Lastly, reduce stray electrical fields by reducing air currents and the
motion of nearby people. Articles that generate strong static electric
fields like sweaters, furs, coats, or long hair should be removed from
the low current measurement area.
Experimental Procedure
Note: The room lights must remain off for the duration of this
experiment.
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1. The first step is to initialize and check the electrometer. No adjustments are needed on the remote preamplifier near the photocell.
Short the input by engaging the input shorting switch (this is the
up position). This switch is useful for momentarily turning off the
meter input when experimental adjustments need to be made. Turn
on the unit by setting the function switch to the + current setting.
Allow a warm up time of 10 minutes. The electrometer measures
currents by reading the voltage across one of three large resistors
whose values are specified on the instrument cover. Under normal
experimental conditions only R2 is required, except for measuring
10 nA where R1 is needed. Set the input resistor switch to R2. The
meter movement and the range switch determine the voltage measured across R2. The current is then found simply from Ohm’s law.
Turn the range switch to the 1 V range. After the instrument has
warmed up, adjust the zero controls until the meter reads zero on
the 1 mV range with the input shorted. Put the range switch back
to 1 V to reduce the chance of an overflow. Using a tissue (not
hands) disconnect the photocell cable from the input and connect
the 10 nA current source instead. Measure the current output from
each of the three current sources using the electrometer. The current is measured by turning off the shorting switch and reducing
the range switch until the meter registers the largest voltage possible without going out of range. If the three current readings are
within the correct orders of magnitude as specified on the current
source then the electrometer is operating properly. Reconnect the
photocell cable (remember, no fingerprints). Always leave the input
shorting switch engaged except when taking a measurement.
2. Turn on and check the adjustable stopping potential. Turn on the
multimeter and the power supply. Set the power supply to 10.0
V. This voltage remains unchanged for the rest of the experiment.
Check that the meter reads the output of the decade divider correctly and that each knob alters the reading by 1 V, 0.1 V, and 0.01
V. Set all knobs on the divider to zero.
3. The monochromator is aligned and adjusted correctly. No adjustments are necessary. Do not bump, jar, or move the monochromator. However a performance test is always appropriate. Power up
the laser and shine it into the entrance slit. The laser wavelength
is 632.8 nm. Rotate the grating until the laser light is visible at the
exit slit. Take note of the monochromator reading of the laser line.
This serves as a monochromator offset calibration which should be
used for all later measurements. Remove the laser and slide the
Tungsten-Halogen lamp forward until it touches the monochromator input slit. Turn on the lamp. The variac voltage for the lamp
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must be set at 110 V, any higher and the lamp will burn out. With
the room lights off, check that the colours visible from the exit slit
are consistent with the monochromator wavelength reading. The
experiment is now ready for operation.
4. Determine the current being emitted by the photocell. It may be
negative, in which case the -current setting is required. This gives a
baseline zero reading for the darkened photocell. You may want to
think about what this current might be if there is one.
5. These measurements will have to be made in darkness. A small
flashlight is used to read and operate the electrometer, divider, multimeter, and monochromator. Keep the flashlight beam away from
the photocell. For as many wavelengths as you feel are necessary (at
least 12), take measurements of the stopping potential of light with
wavelengths ranging from 420 nm to 600 nm. Use a consistent criterion to detect when the photocurrent has stopped. The best method
is to simply adjust the divider until the needle reads zero, without
changing the range setting of the electrometer. The Fluke multimeter reads out the potential Vs . The monochromator dial indicates
the wavelength in nm. Notice that the current jumps wildly when
people move near the photocell or when the divider is adjusted.
The method to use is to make a divider adjustment and then move
away and stay still until the electrometer stabilizes. Make further
adjustments to the decade divider as required until a zero current
reading is obtained.
6. Perform one of the optional investigations.
Error Analysis
As discussed in the theory section, there are many variables that
affect the outcome of this experiment which are not under the control of the experimenter. No error analysis for these effects is required.
Once the monochromator offset is found using the laser, the maximum
wavelength error over the 400 nm to 600 nm range will be ±1.0 nm. Estimate a reasonable error for the stopping potential. This will not be an
instrument error. Rather, it will reflect the uncertainty of finding the
actual zero current point that represents the stopping potential. For
current measurements, the uncertainty is propagated from the voltage
uncertainty (half the smallest division on the meter) and the resistor
uncertainty. The resistor uncertainty can be estimated from the number of significant figures that specify the resistor values on the cover of
the electrometer. For example, two significant figures implies an error
on the order of ±5 in the next smaller digit position. The wavelength
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error and stopping potential error will propagate to an error in the
slope from which Planck’s constant is found.
To be handed in to the laboratory instructor
Prelab
1. List and briefly discuss three significant considerations when measuring very small currents.
2. Describe what is meant by photocell dark current.
3. The resistors R1, R2, and R3 together with the voltage range switch
determine the currents the electrometer can measure. The range
switch extends from a 30 V scale down to a 1 mV scale. The electrometer resistor values are R1 = 0.93 × 108 Ω, R2 = 0.92 × 1010 Ω,
and R3 = 0.90 × 1012 Ω. What is the largest and smallest current
range on the electrometer? Write your answer once with scientific
notation and once with proper SI prefixes.
Data Requirements
4. Record your observations of the current measured by the electrometer when you bend, twist, and/or vibrate the wire connecting the
photocell to the input of the electrometer. Note, do NOT exert large
forces or displacements on the wire when making these observations, it is not necessary and damages the apparatus.
5. A table of values with uncertainties for the three reference current
sources as well as the dark photocell current reading.
6. A value for the wavelength of laser light as measured using the
monochromator. A table of the colors observed versus their wavelength from the Tungsten-Halogen lamp.
7. Table of values for the stopping potentials, wavelengths, frequencies and their uncertainties. Include the measured current with a
stopping potential of zero (dark current).
8. A graph of stopping potential versus frequency with error bars, and
a determination of the slope and intercept (with uncertainties).
9. Any one of the following:
(a) Glass can reflect ultraviolet radiation but not transmit it. Quartz
can transmit and reflect ultraviolet light. The Tungsten-Halogen
bulb is made from quartz. The photocell and the monochromator
are made from glass. Take readings on stopping potentials from
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420 nm to 260 nm. Report and explain your observations. What
is the minimum change needed to make this experiment work in
the ultraviolet light range?
(b) Design and implement an experiment to check whether the stopping potential really is independent of light intensity but the photocurrent really is not. Report your observations and conclusions.
(c) Design and implement an experiment to measure the intensity
of the Tungsten-Halogen lamp at different wavelengths. Present
your observations and conclusions.
(d) For one given wavelength, plot photocurrent versus stopping
potential. Include a table of values with your graph. Discuss
whether your data supports the assertion that raising the stopping potential retards the photocurrent.
Discussion
10. Based on your graph in #8 above, discuss what the slope represents.
From your data, determine an experimental value for Planck’s constant and compare this to the accepted value. Briefly discuss in your
own words why the value you calculated for the intercept is likely
not an accurate measurement of the work function for the photocathode material.
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