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PC1144 Physics IV
Photoelectric Effect
1
Objectives
• Demonstrate the different predictions of the classical wave and quantum model of light
with respect to the photoelectric effect.
• Determine an experimental value of Planck’s constant.
2
Equipment List
• Mercury vapour light source
• PASCO h/e apparatus
• Yellow/Green filter
• Variable transmission filter
• Digital voltmeter
3
Theory
The photoelectric effect is the emission of electrons from the metal surface when light strikes
the surface. This effect is used in many devices, including TV cameras, camcorders and night
vision viewers. In 1905, Albert Einstein presented an explanation of the photoelectric effect
which simply cannot be understood without quantum physics. It was primarily for his theory
of the photoelectric effect that he was awarded the Nobel Prize in Physics in 1921.
The photoelectric effect was observed by Heinrich Hertz in 1887. The particle theory of
light seemed to be doomed after James Clerk Maxwell’s prediction of electromagnetic waves
that move at the speed of light together with Thomas Young’s double slit interference experiment. Hertz was able to produce and detect electromagnetic waves of varying wavelengths
in accordance with Maxwell’s theory. However, he noticed that a spark would jump more
readily between two electrically charged spheres when their surfaces were illuminated by the
light from another spark during his experiments. He offered no explanation for this observed
phenomenon.
One year later, 1888, another German physicist, Wilhelm Hallwachs, followed up on this
investigation with his experiments. In his experiment, a clean circular plate of zinc was
mounted on an insulating stand and attached by a wire to a gold leaf electroscope, which was
then charged negatively. The electroscope lost its change very slowly. However, if the zinc plate
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was exposed to ultraviolet light, charge leaked away quickly. If the plate is positively charged,
there was no fast charge leakage. Further investigation by others showed that ultraviolet
light actually caused electrons to be ejected from the metal surface. Although Hallwach’s
experiment clarified the situation, he did not offer any explanation too.
In 1902, Phillip von Leonard, an assistant of Hertz, was able to show that the energy of
the ejected electron was not related to the intensity of the light but was rather related to the
wavelength of the light used. This caused problems for the classical wave model. According
to the classical wave model, the intensity is related to the magnitude of the electric field
(i.e. I ∝ E 2 ). Thus, the magnitude of the electric field should increase by increasing the
intensity of the light. The greater the electric field, the greater the force on the electrons in
the metal. Therefore, more work should be done on the electrons and this should give them
a greater kinetic energy. However, Leonard’s results proved that the kinetic energy of the
ejected electrons is independent of the light intensity.
In the classical theory, the photoelectric effect should occur for any frequency of the light
provided that the light is intense enough to give the energy required for the electrons to escape
from the metal surface. However, Leonard showed that for each surface material, there is a
cutoff frequency, f0 . For frequencies less than f0 , the photoelectric effect will not happen no
matter how intense the illumination. Also, it is expected that there should be a measurable
time lag between the light arriving at the metal surface and the electrons escaping from the
metal. The electrons need to accumulate enough energy to escape from the metal surface.
This accumulation should take some time if the light is dim since the light energy is uniformly
distributed over the wavefront according to classical theory. However, no detectable time lag
was ever measured.
Einstein resolved the problems with a straightforward explanation of the effects seen by
others. Based on an assumption made five years earlier by Max Planck, he postulated that a
beam of light consists of a collection of discrete packets of energy called photons. Each photon
contains an amount of energy E given by
E = hf
where f is the frequency of the light and h is a fundamental constant of nature called Planck’s
constant. When light shines on a metal, a photon arriving at the surface can give up its energy
to an electron in the metal. This energy transfer is an all-or-nothing process. The electron
gets all the photon’s energy or none at all. If the photon has enough energy to do the work of
removing the electron from the metal, the electron can be ejected. The work required depends
on how strongly the electron is held. For the least strongly held electrons, the necessary work
has a minimum value φ and is called the work function of the metal. If a photon has energy in
excess of the work needed to remove an electron, the excess energy appears as kinetic energy
of the ejected electron. Thus, the least strongly held electrons are ejected with the maximum
kinetic energy KEmax .
Einstein applied the principle of conservation of energy and proposed the following relation
to describe the photoelectric effect:
KEmax = hf − φ .
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Since the work function, which is the energy required to release an electron from the metal
surface, is a constant for any given material, the maximum kinetic energy depends directly on
the frequency of the incoming light. It is also clear that there is a minimum light frequency
for a given metal, for which the photon energy is equal to the work function. Light below that
frequency, no matter how intense, will not cause photoelectric effect.
Figure 1: A schematic diagram of the photoelectric effect apparatus.
A schematic of the photoelectric effect apparatus is shown in Figure 1. The emitter is
a light sensitive material and placed in a transparent evacuated tube along with a collector.
This device is then connected to a variable voltage source which allows the generation of an
adjustable (uniform) electric field between the emitter and the collector. As light is incident on
the light sensitive emitter, the escaping electrons from the emitter with initial kinetic energy
could travel to the collector and thus a current would flow through the circuit.
By applying a negative potential to the collector plate (relative to the emitter), the electrons could be prevented to reach the collector plate. If the potential applied to the collector
is gradually increased, the electrons ejected from the emitter would not have enough energy
to reach the collector. At a certain threshold voltage, also known as the stopping potential,
V0 , there is no current flowing through the circuit. At this point, the maximum kinetic energy
of the electrons is equal to the electrical potential energy, i.e. KEmax = eV0 . We thus have
eV0 = hf − φ ,
where e is the electron’s charge. It would be extremely difficult to measure directly the
maximum kinetic energy of the ejected electrons. However, by relating the maximum kinetic
energy to the stopping potential, this quantity can easily be measured.
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Theory of operation
In experiments with the h/e Apparatus, monochromatic light falls on the cathode plate of a
vacuum photodiode tube that has a low work function φ. Photoelectrons ejected from the
cathode will be collected on the anode.
The photodiode tube and its associated electronics have a small capacitance which becomes
charged by the photoelectric current. When the potential on this capacitance reaches the
stopping potential of the photoelectrons, the current decreases to zero, and the anode-tocathode voltage stabilizes. This final voltage between the anode and cathode is therefore the
stopping potential of the photoelectrons.
To measure the stopping potential, the anode is connected to a built-in amplifier with
an ultrahigh input impedance (> 1013 Ω), and the output from this amplifier is connected
to the output jacks on the front panel of the apparatus. This high impedance, unity gain
(Vout /Vin = 1) amplifier is used to measure the stopping potential with a digital voltmeter.
Due to the ultra high input impedance, once the capacitor has been charged from the
photodiode current it takes a long time to discharge this potential through some leakage.
Therefore, a shorting switch labeled “PUSH TO Zero” can be used to quickly bleed off the
charge. However, the op-amp output will not stay at 0 volts after the switch is released since
the op-amp input is floating.
Due to variances in the assembly process, each apparatus has a slightly different capacitance. When the zero switch is released, the internal capacitance along with the user’s body
capacitance coupled through the switch is enough to make the output voltage jump and/or
oscillate. Once photoelectrons charge the anode the input voltage will stabilize.
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Photoelectric Effect
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Laboratory Work
Equipment setup
Set up the equipment as shown in Figure 2. Please familiarize with the various parts of the
equipment as indicated in Fig 2. Switch on the light source for five minutes to warm up before
any measurement is taken.
Figure 2: Equipment setup using a mercury vapor light source and the h/e apparatus.
Set the h/e apparatus directly in front of the mercury vapor light source. The diffraction
grating in the lens/grating assembly produces a spectrum pattern to the left and to the right.
The grating is blazed to produce the brighter spectrum on one side only as shown in Figure 3.
Move the h/e apparatus so that the brighter spectrum pattern appears on the white reflective
surface of the apparatus.
Tilt the light shield of the apparatus out of the way to reveal the white photodiode mask
inside the apparatus as shown in Figure 4. Slide the lens/grating assembly back and forth
on its support rods until the sharpest image of the aperture centered on the hole in the
photodiode mask. Secure the lens/grating assembly by tightening the thumbscrew.
The white reflective mask on the h/e apparatus is made of special fluorescent material.
This allows the ultraviolet line to be seen as a blue line and it also makes the violet line appear
more blue. The actual colours of the light can be seen if a piece of white non-fluorescent
material is held in front of the mask.
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Figure 3: A schematic diagram of the spectrum.
Figure 4: A schematic diagram of the light shield.
Turn the power switch ON. Align the h/e apparatus on its support base so that the same
spectral maxima that falls on the opening in the white reflective mask also falls on the window
in the photodiode mask with no overlap of colour from other spectral lines. It is important
that only one colour falls on the photodiode window when making measurements. Return the
light shield to its closed position.
Check the polarity of the leads from your digital multimeter (DMM) and connect them
to the OUTPUT terminals of the same polarity on the h/e apparatus. Press the “PUSH TO
ZERO” button on the side panel of the h/e apparatus to discharge any accumulated potential
in the unit’s electronics. This will assure the apparatus records only the potential of the light
you are measuring. Read the output voltage on your DMM and it is a direct measurement
of the stopping potential for the photoelectrons. Note that the reading of stopping potential
will fluctuate before it drops down to the actual stopping potential voltage.
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Part A: Classical wave model versus quantum model of light
According to the quantum theory of light, the maximum kinetic energy, KEmax , of the ejected
electrons depends only on the frequency of the incident light, and is independent of the
intensity. Thus, the higher the frequency of the light, the greater its energy. In contrast, the
classical wave model of light predicted that KEmax would depend on light intensity. In other
words, the brighter the light, the greater its energy.
This experiment investigates both of these assertions. Two spectral lines from a mercury
light source are selected and maximum kinetic energy of the ejected electrons as a function
of the intensity is investigated. Different spectral lines with two different intensities are then
selected maximum kinetic energy of the ejected electrons as a function of the frequency of the
light is investigated.
SAFETY: DO NOT touch the surface of the mercury housing as it is very HOT during
the experiment.
Electron maximum kinetic energy versus light intensity
A-1. Adjust the h/e apparatus so that only one of the first order spectral colours falls upon
the opening of the mask of the photodiode. Whenever you use green or yellow spectral
line, place the corresponding coloured filter over the white reflective mask on the h/e
apparatus. Record the colour used in Data Table 1.
Note: When making measurements it is important that only one color falls on the
photodiode window. There must be no overlap from adjacent spectral maxima.
Note: These filters limit higher frequencies of light from entering the h/e apparatus.
This prevents ambient room light from interfering with the lower energy yellow and
green light and masking the true results. It also blocks the higher frequency ultraviolet
light from the higher order spectra which may overlap with lower orders of yellow and
green.
A-2. Place the variable transmission filter in front of the white reflective mask (and over
the coloured filter if one is used) so that the light passes through the marked section
100% and reaches the photodiode. Press the “PUSH TO ZERO” button and release it.
Record the stopping potential as given by the DMM voltage reading when it stabilizes
in Data Table 1.
A-3. Move the variable transmission filter so that the next section (e.g. 80%) is directly in
front of the incoming light. Again, press the “PUSH TO ZERO” button, release it and
record the new DMM reading after it has stabilized in Data Table 1.
Note: If necessary, WAIT till the voltage reading stabilize before taking the measurement. The time to reach full voltage increases dramatically with decreasing intensity
(up to a minute for 20% intensity). Due to the leakage of charge through the zero-gain
amplifier, it is expected to have a slight drop in the measured stopping potential. As
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the intensity decreases, the equilibrium point between the electrons arriving and the
electrons leaving through the amplifier becomes lower.
A-4. Repeat step A-3 until you have tested all five sections of the filter (100%, 80%, 60%,
40% and 20%).
A-5. Repeat steps A-1 through A-4 using a second colour from the mercury light spectrum.
Record your data in Data Table 1.
Electron maximum kinetic energy versus Light frequency
A-6. Five colours in the first order mercury light spectrum can be seen easily. Adjust the
h/e apparatus so that only the colour band falls upon the opening of the mask of the
photodiode. Place the yellow coloured filter over the white reflective mask on the h/e
apparatus.
A-7. Place the variable transmission filter in front of the white reflective mask (and over the
coloured filter if one is used) so that the light passes through the marked section 100%
and reaches the photodiode. Press the “PUSH TO ZERO” button and release it. Record
the DMM voltage reading (stopping potential) when it stabilizes in Data Table 2.
A-8. Repeat the process for each colour in the first order spectrum. Be sure to use the green
filter when measuring the green spectrum.
A-9. Repeat steps A-6 through A-8 by passing the light through the marked section 80% on
the variable transmission filter. Record your data in Data Table 2.
Part B: Determination of the Planck’s constant
According to the quantum theory of light, the energy of light is directly proportional to its frequency. Thus, the higher the frequency, the more energy it has. With careful experimentation,
the constant of proportionality, Planck’s constant, can be determined. The characteristics of
the metal, work function, can also be determined.
In this experiment, you will select different spectral lines from two orders of the mercury
light spectrum and investigate the maximum kinetic energy of the ejected electrons as a
function of the wavelength and frequency of the light.
B-1. Five colours in two orders of the mercury light spectrum can be seen easily. Adjust the
h/e apparatus carefully so that only one colour from the first order (the brightest order)
falls on the opening of the mask of the photodiode.
B-2. For each colour in the first order spectrum, record the DMM voltage reading (stopping
potential) when it stabilizes in Data Table 3. Use the yellow and green coloured filters
on the reflective mask of the h/e apparatus when you measure the yellow and green
spectral lines.
B-3. Move to the second order and repeat the process. Record your data in Data Table 3.
Last updated: Monday 2nd February, 2009 1:09pm (KHCM)
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