PHYSICS 320 LABORATORY
THE PHOTOELECTRIC EFFECT
OBJECT:
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.
APPARATUS:
A Mercury Vapor Light Source,
a special h/e apparatus with a photodiode tube, a digital
voltmeter, a digital oscilloscope, green and yellow filters, and a New Focus variable transmission filter
wheel.
BACKGROUND:
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 = hn
where E equals the radiant
energy, n 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 = hn
= KEmax +f
where KEmax is
the maximum kinetic energy of the emitted photoelectrons, and f
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 f
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:
hn
= Ve + +f
When solved for V, the equation
becomes:
V = (h/e) n
- ( f /e)
Thus, a plot of V versus ν for different frequencies of light will yield a linear plot with
a slope (h/e) and a V intercept of (-
f /e).
Setup Procedure:
-
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.
-
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. 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. Read the voltage on the digital voltmeter. 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 2.5 seconds 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. You can
use the oscilloscope cursors to measure voltage and time.
Experiment 1: Wave
Model versus Quantum Model
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 results with different light frequencies.
Procedure:
-
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 wheels in front of
the entrance aperture so that the light passes through both filters at normal
incidence before
it reaches the photodiode. 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.
Save the oscilloscope waveform on the computer and record the final DVM voltage reading in the table
below.
-
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, try to
obtain oscilloscope traces that have similar peak heights.
-
Repeat step 3 for filter wheel settings that reduce
the intensity by a factor of 100 and 1000.
- Repeat the procedure using the yellow light from the spectrum.
Be sure to use the yellow filter to remove any stray non-yellow light.
|
Green light |
|
%Transmission |
Stopping
Potential |
Approx. Charge Time |
100 |
|
|
80 |
|
|
60 |
|
|
40 |
|
|
20 |
|
|
|
Yellow light |
|
%Transmission |
Stopping Potential |
Approx. Charge Time |
100 |
|
|
80 |
|
|
60 |
|
|
40 |
|
|
20 |
|
|
Analysis
-
Describe the effect that passing
different amounts of the same color of light through the Variable Transmission
Filter Wheel has on the stopping potential and thus the maximum energy of the
photoelectrons, as well as the charging time.
-
Describe the effect that different
colors of light had on the stopping potential and thus the maximum energy
of the photoelectrons.
-
Defend whether this experiment
supports a wave or a quantum model of light based on your lab results.
Experiment #2: Determining
Planck's Constant
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
light.
Procedure:
-
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
the photodiode.
-
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
second order.
Color |
Stopping Potential
First Order |
Stopping Potential
Second Order |
Yellow |
|
|
Green |
|
|
Blue |
|
|
Violet |
|
|
Ultraviolet |
|
|
Analysis:
-
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 f/e
ratio. Then, calculate h and f.
-
In your conclusions, discuss
your results with an interpretation based on a quantum model of light.
COLOR |
WAVELENGTH |
Yellow |
579.0
nm (average) |
Green |
546.1
nm |
Blue |
435.8
nm |
Violet |
404.7
nm |
Ultraviolet |
365.5
nm |