PHOTOELECTRIC EFFECT
THEORY
V0
When light of sufficiently high frequency falls on the
surface of a metal, electrons are emitted. It is
observed that the maximum kinetic energy that may
be attained by these electrons, KEmax, depends upon
the frequency of the light and the characteristics of
the metallic surface. One can determine KEmax by
measuring the minimum voltage V0 (stopping
potential) necessary to prevent all photoelectrons
from escaping from the metal. The relationship
between KEmax and V0 is given by Equation 1.
KEmax = eV0
1
Slope = h/e
0
fc
f
 /e
where e = magnitude of the electron’s charge.
It is also observed that a "cutoff frequency", fc, exists
for each metal such that no photoelectrons will be
emitted if the frequency of the incident light is less
than fc, regardless of the light intensity.
To explain the effect, Einstein assumed that light is
quantized, i.e., it consists of indivisible packets of
energy called photons. Each photon has energy E=hf
where h = Planck's constant and f = frequency. This
assumption served as the basis for the derivation of
Equation 2.
KEmax = hf - φ
2
where  = work function of the metal. The work
function is the minimum amount of energy that an
electron must gain in order to escape from the metal.
Use equations 1 and 2 to write an expression for V0
as a function of frequency.
The plot of stopping potential vs frequency is a
straight line (See Fig. 1), with a slope of h, a yintercept of , and an x-intercept of fc.
In this experiment, V0 will be measured for several
frequencies of light and this data will be used to
determine values for h, fc, and .
Figure 1
PROCEDURE
Turn on the light source and allow it to warm up for a
few minutes. A diffraction grating spreads the
emitted light into a characteristic spectrum,
separating light of different frequencies. You can
observe the first- and second-order mercury spectral
lines on the white reflective mask of the h/e apparatus
as it is rotated to the right and left of the centerline
from the mercury source. The frequencies of the
observable spectral lines are given in Table I.
Note: The white reflective mask on the h/e apparatus
is made of a special fluorescent material in order that
you can see the ultraviolet line (violet #2) which will
appear as a blue line. The violet line (violet #1) will
also appear more blue. You can see the actual colors
of the light if you hold a piece of white nonfluorescent material in front of the mask.
It is important when taking data, that only one
spectral line falls on the photodiode window
inside the apparatus. There must be no overlap
from adjacent spectral lines, so that you can
measure Vo corresponding to a single frequency.
PHOTOELECTRIC EFFECT
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Table I
MERCURY SPECTRAL LINES
Color
Violet #2
Violet #1
Blue
Green
Yellow
Frequency (Hz)
8.20 x 1014
7.41 x 1014
6.88 x 1014
5.49 x 1014
5.19 x 1014
bars. Be sure to scale your graph and extend your
best-fit line, to clearly illustrate both the x- and yintercepts. Fit the graph to determine the values of h,
, and fc, along with the error in each value.
Compare your value of h to the standard value, and
comment on whether your value is within
measurement error of the standard.
Now similarly measure the stopping potential for the
five second-order spectral lines, once again getting
six Vo values for each frequency. Determine the
average stopping voltage Vave for each frequency, and
determine the standard deviation of the mean m.
Determine the stopping voltage, Vo, for each of the
spectral lines listed in table I. To do this, rotate the
apparatus around the light source and rotate the box
on its stand until the line of interest is focused on the
aperture inside the apparatus. Be sure that the light
shield is closed whenever taking data, to prevent
stray light of other frequencies from entering the
window. Press the ZERO button on the side panel of
the h/e apparatus (near the ON/OFF switch) to
discharge any accumulated potential in the unit's
electronics. Read the output voltage on the digital
voltmeter. (The voltmeter should be on the lowest
setting for which it is not overloaded.) Wait until the
voltmeter has stabilized at a constant value before
recording the voltage.
Important: Use the appropriate filters when making
measurements with the green and yellow spectral
lines.
Do this procedure for each of the five first-order
spectral lines given in Table I, both on the right and
on the left. Then repeat the measurement of these
first-order-line stopping voltages two more times for
each color on each side. Do not just leave the
apparatus in place and take several measurements –
the placement of the apparatus can lead to systematic
error. You should have six values of Vo for each
frequency.
Is the error for the second-order values better or
worse than for first-order?
Based on your
observation of the spectral lines, does this make
sense? Explain.
Create a new plot of Vave vs frequency, this time
plotting two points for each frequency – the 1st-order
value and the 2nd-order value – including error bars
for each. Fit the graph to determine the values of h,
, and fc, along with the error in each value.
Did you get more accurate values for h, , and fc by
including the less-accurate 2nd-order data? Does this
make sense? Explain.
Do you think that including extra data will always
increase accuracy, even if the data is less accurate? It
might help to make a graph of your good data along
with fake data with ridiculously large error bars, and
see what happens to the error in your fit values.
Determine the average stopping voltage Vave for each
frequency, and determine the standard deviation of
the mean m. Plot Vave vs frequency, including error
PHOTOELECTRIC EFFECT
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