PHYSICS 320 LABORATORY
THE PHOTOELECTRIC EFFECT
To study the emission of
electrons from a metal surface which is irradiated with light. To experimentally
determine the value of Planck's constant "h" by making use
of the spectral dependency of the photoelectric effect.
A Mercury Vapor Light Source,
a special h/e apparatus with a photodiode tube, a digital
voltmeter (DVM), a digital oscilloscope, green and yellow filters, and a New
Focus variable transmission filter wheel.
In 1901 a German physicist
Max Planck published his law of radiation. Planck went on to state that
the energy lost or gained by an oscillator is emitted or absorbed as a
quantum of radiant energy, the magnitude of which is expressed by the equation:
E = hf
where E equals the radiant energy, f is the frequency of
radiation, and h is a fundamental constant, now known as Planck's constant.
Albert Einstein applied Planck's
theory and explained the photoelectric effect in terms of the quantum model
using his famous equation for which he received the Nobel Prize in 1921:
E = hf
= KEmax + (phi)
where KEmax is
the maximum kinetic energy of the emitted photoelectrons, and (phi)
is the energy needed to remove them from the surface
of the material (the work function). Here E is the energy supplied by the
quantum of light known as a photon.
In the h/e experiment, light photons with energy hn are incident upon the cathode of a vacuum
tube. The electrons in the cathode use a minimum (phi) of their energy to escape, leaving the surface with a maximum energy
of KEmax. Normally
the emitted electrons reach the anode of the tube, and can be measured
as the photoelectric current. However, by applying a reverse potential
V between the anode and cathode, the photoelectric current can be stopped.
KEmax can then be determined by measuring the minimum
reverse potential needed to bring the photoelectric current to zero. Thus,
Einstein's relation becomes:
= Ve + (phi)
When solved for V, the equation
V = (h/e)f
Thus, a plot of V versus f for different frequencies of light will yield a linear plot with
a slope (h/e) and a V intercept of [-(phi)/e].
Experiment 1: Wave
Model versus Quantum Model
Connect a digital voltmeter
(DVM) to the output terminals of the h/e apparatus. Select
the 2V range on the meter.
Direct a beam of light from
the Mercury Vapor source toward the h/e apparatus and focus
the light onto the white reflective mask about the entrance slit. Make
sure that the light passes from the source through the center of the diffraction
grating/lens. NOTE: The Mercury source emits UV light - Please wear eye
Roll the cylindrical light shield,
just behind the slit, out of the way to reveal the white photodiode mask
inside the Apparatus. Move the h/e Apparatus until the light
passes through the entrance slit and produces an image centered on the
dark window in the photodiode mask. Focus the light until you achieve the
sharpest possible image on the photodiode window. Be sure that the
photodiode assembly is secure on its post and will not rotate (the screw on the
postholder should be tight). Then rotate the cylindrical
light shield back into position.
Turn the power switch ON. Move
the apparatus to select one of the colored maximums to pass directly into
the h/e Apparatus through the slot in the white reflective
mask and onto the window of the photodiode mask.
Press the red zero button on
the side panel of the Apparatus and hold for a second to discharge any accumulated charge in
the unit's electronics. Release the button and wait for the reading on the digital voltmeter
to settle. This
is a direct measurement of the stopping potential for the photoelectrons.
You may observe the charging time of the vacuum
photodiode tube by connecting a digital oscilloscope to the output terminals.
Make sure that the ground connection is correct. Put the scope on
auto-trigger with DC coupling, the time base at 250 ms per division, and the vertical scale on
~500mV per division. Depress the zero button for a second or two and
release it. Observe the waveform on the oscilloscope. Note the zero
voltage time when the button was depressed, the fast increase in voltage when the
button was released, and the ~ exponential settling of the charge. Note that
use the oscilloscope cursors to measure voltage and time.
According to the photon theory
of light, KEmax for photoelectrons depends only on the frequency
of the incident light, and is independent of intensity. Thus the higher
the frequency, 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 the energy.
This lab investigates these
assertions. The experiment selects two spectral lines from a mercury line
source and investigates KEmax versus intensity. The different
spectral lines show if KEmax changes with different light frequencies.
Adjust the h/e
apparatus so that only green light passes through the entrance
slot and falls on the opening of the mask of the photodiode. Place the green colored filter
over the entrance aperture.
Now place the New Focus filter wheel holder right in
front of the entrance aperture so that the light passes through both filters at
normal incidence just before
it reaches the photodiode. The filters must be as close as possible to the
detector to minimize the impact of stray room light. BE CAREFUL NOT TO TOUCH THE OPTICAL SURFACES
OF THE FILTERS. Rotate both filter wheels to the 0.04 transmission
setting. Press the instrument discharge button, release it, and observe on
the oscilloscope the time required to recharge the instrument to the maximum voltage.
When you have a good, complete trace on the oscilloscope, save the waveform
the computer (open OpenChoice Desktop, select the GPIB instrument and the
Waveform Data Capture tab, then Get and Save the data) and record the final steady-state DVM voltage reading.
Rotate both filter wheels to the 0.5 transmission
setting. Note that if x and y are the wheel settings, the
transmission is reduced by the factor 10(x+y) so the light is
reduced by a factor of 10 in this case. Observe the recharging time on the
oscilloscope for this intensity, save the waveform on the computer, and
record the final DVM reading. Note that the charging process is very
sensitive to how the zero button is released. For best results when
comparing different intensities, you should try to obtain oscilloscope traces that
begin at the same time and have
similar initial peak heights.
Repeat step (3) for filter wheel settings that
reduce the intensity by a factor of 100.
- Repeat the procedure using the yellow light from the spectrum.
Be sure to use the yellow filter to remove stray light.
For each color, plot the 3 oscilloscope
measurements (with factors of 1, 10, and 100 intensity reduction) together
on a single graph of voltage vs. time. Shift the time axes so that the
button release times are approximately coincident and the responses can be compared.
You may also want to remove any initial vertical drop and normalize each of the
curves (i.e. divide each voltage by the maximum voltage) to correct for any
differences in starting conditions.
Describe the effect that passing
different amounts of the same color of light through the Variable Transmission
Filter Wheel has on the charging time. Should the stopping potential and
thus the maximum energy of the photoelectrons depend on the intensity of the
incident light? If your experimental results are inconsistent with your expectations,
explain why your low intensity measurements might be inaccurate.
At each intensity, compare the stopping potential for
the green and yellow light. For a given intensity, does the measured energy of the
photoelectrons depend on the color of the light?
Based on your lab results, discuss whether this experiment
supports a wave or a quantum model of light.
Experiment #2: Determining
In this experiment you will
select different spectral lines from mercury and investigate the maximum
energy of electrons as a function of the wavelength and frequency of the
Adjust the h/e
apparatus so that only one color of light falls on the opening mask of
the photodiode and that the light coming through the slit strikes the center of
Record the DVM voltage reading
(stopping potential) in the table below.
Repeat the process for each
color in the spectrum. Be sure to use the yellow or green filter when measuring
for the yellow or green spectral line, respectively. Do not use a filter
for the blue and uv lines.
Repeat the process for the same colors in the
Put this data on a spreadsheet.
Add columns to indicate the wavelength and the frequency of each spectral
line. Plot a graph of the stopping potential vs. frequency.
Perform a regression on the
data to determine the slope and y-intercept. Interpret the results in terms
of the h/e ratio and the [(phi)/e]
ratio. Then, calculate h and (phi). Compare your experimental h to the accepted value. To what wavelength does your value of (phi) correspond?
In your conclusions, discuss
your results in the context of the wave and quantum models of light.