Student Name and I.D.: Peter
Lab session: Lab 2B
Submission
Date: 28-2-2001
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1.
Introduction
One of the experiments that classical
picture of electromagnetic waves is unable to explain is the photoelectric
effect.
This
experiment aims to determine experimentally the Planck’s constant and the
Intensity dependence of photocurrent.
2.
Theory
Photoelectric effect is the emission
of electrons by matter due to the action of incident light.
The voltage at which the current vanishes is called the stopping potential or the backing voltage and is related to the maximum kinetic energy of the photoelectrons by the energy relation,
mvm2 = eVo
where
vm is the maximum vellcoity which any electron has when it leaves the
photosensitive surface, Vo is the voltage at which the current is
reduced to zero, and e and m are the charge and mass of the electron
respectively.
In terms of the quantum or photon nature of light, each photo has an energy hν, where h is Planck’s constant and νis the frequency of the incident light. In the photoelectric effect all or none of the energy hνis transferred to an electron in the metal. Some of the energy the electron may acquire is used in escaping from the metal. This energy is called the work function and represented by Φ. The rest of the energy supplied by the photon goes into kinetic energy of the electron. From these considerations, we have the following relation:
hν= ½
mvm2 + Φ = e Vo + Φ
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[1]
3.
Procedure
The electrical connections shown in Figure 1 were made.
Figure 1: Electrical Connection For
Measuring Planck’s constant
Part I: Determination of Planck’s constant
The equipment were setup as shown in Figure 2.
Figure 2: Arrangement of Apparatus for Part A
Figure 3: Optical part used in the experiment
The board band colour filter (a set of 6 shown in Figure 3) were placed one by one on the cell window. For each filter, with the backing-off voltage set to zero, the large signal on the electrometer was observer when the lamp illuminates the photocell. The magnitude of the signal was recorded. The backing-off voltage was gradually increased until the signal on the electrometer became zero and the wavelength of the filter and backing-off voltage were recorded.
The above steps were repeated with
narrow band colour filter but the mercury lamp was used as light source.
Part II: Intensity dependence of photocurrent
The pinhole in the front of the photocell was inserted and mercury violet filter was inserted in front of the pinhole. The polarizers was then placed in front of the apparatus window, as shown in Figure 4.
Figure 4: Arrangement of apparatus for Part II
The backing-off voltage was set to be
zero and the output voltage of the electrometer was adjusted. The polarizer
angle was varied from 0o to 180o and the photoelectric
current was recorded.
4.
Result and Analysis
Part A: Determination of Planck’s
constant
For board band colour filter,
A graph of backing-off voltage versus frequency is plotted.
Figure 5: Backing-off voltage versus
frequency (Board band colour filter)
The graph is a straight line. Hence
backing-off voltage has a linear relation with the frequency.
From equation [1],
Planck’s constant, h = slope x
e = 0.2495 x 10-14 x 1.602 x 10-19
Cut-off frequency, ν=
3.5 x 1014 Hz
Work function = hν
= 1.4 eV
For narrow band colour filter,
A graph of backing-off voltage versus frequency is plotted:
Figure 6: Backing-off voltage versus
frequency (narrow band colour filter)
The graph is a straight line. Hence
backing-off voltage has a linear relation with the frequency.
From equation [1],
Planck’s constant, h = slope x
e = 0.2858 x 10-14 x 1.602 x 10-19
Cut-off frequency, ν= 3.488 x 1014 Hz
Work function = hν=
1.598 eV
Part II: Intensity dependence of
photocurrent
The graph of the voltage of the electrometer versus polarizer angle is plotted. The cosine function is also plotted on the same graph.
Figure 7: voltage of the electrometer
versus polarizer angle
Now consider,
Figure 8: Intensity versus polarizer angle
From the graph in Figure 8, the
straight is not a horizontal, which is inconsistent with the expected result (a
horizontal line). This is due to the error in photocell.
5.
Error Analysis
In Part A,
For Board band filter:
By Excel,
Δ h = (Δ slope / slope) x h
= (0.0377 / 0.2495) x 3.997 x 10-34
= 0.54 x 10-34 Js
Hence h = (4.0 + 0.5) x 10-34
Js
Δ Ф = (Δ y-intercept / y-intercept) x Ф
= (0.2098 / 0.8733) x 1.4
= 0.336 eV
Hence Ф = 1.4 + 0.3 eV
For narrow band filter:
By Excel,
Δ h = (Δ slope / slope) x h
= (0.0237 / 0.2858) x 4.58 x 10-34
= 0.38 x 10-34 Js
Hence h = (4.6 + 0.4) x 10-34
Js
Δ Ф = (Δ y-intercept / y-intercept) x Ф
= ( 0.1397 / 0.997) x 1.598
= 0.224 eV
Hence Ф = 1.6 + 0.2 eV
6.
Discussion
1) The experimental value of the Planck’s constant is smaller than the accepted value (6.63 x 10-34). This is due to the error source in the experiment.
For board band colour filter, percentage difference = 26.32%
For narrow band colour filter, percentage difference = 10.46%
The data
form the narrow band colour filters is more accurate than that from board band
colour filters. This is because at higher wavelength, light is more capable to
eject electrons.
2) The theoretical value of the work function of Cesium is 1.9 eV. The experimental value is smaller than the theoretical one.
For board band colour filter, percentage difference = 26.32%
For narrow
band colour filter, percentage difference = 15.79%
3)
When light falls onto the surface of a metal it can liberate electrons
from the metal, forming a photoelectric current. When the intensity of the light
falling on the cathode is increased, while keeping the wavelength constant, the
greater intensity and corresponding greater electric and magnetic field
strengths give some electrons more energy than they had before.
4)
The kinetic energy of the emitted electrons remains the same as long as
the wavelength of the incident light is not changed. Increasing the intensity of
the light serves only to increase the photoelectric current. Therefore light is
quantized.
5) In classical wave theory, the maximum kinetic energy should be proportional to the intensity of the radiation. Also, the photoelectric effect should occur for light of any frequency or wavelength. The first electrons should also be emitted in a time interval of the order of seconds after the radiation first strikes the surface.
The
experimental results suggest the failure of the wave theory to account for the
photoelectric effect. First, the maximum kinetic energy is totally independent
of the intensity of the light source. Doubling the intensity of the source
leaves the stopping potential unchanged, indicating no change in the kinetic
energy of the electrons. Second, the photoelectric effect does not occur at all
if the frequency of the light source is below a certain value. Third, the first
photoelectrons are emitted virtually instantaneously after the light source is
turn on.
7.
Error sources
Source of errors includes:
a) The room is not dark enough. If the room is totally darkness, we will have difficulty in recording data.
b)
Errors in photocells, which is due to improper use from the previous
users.
8.
Suggestions and improvements
Precautions:
1)
Do not place the filters directly in front of the mercury lamp. The lamp
is very hot and will melt the filters if you do so.
2)
The cell window is covered by a black plate to prevent the cell from
being exposed to the light directly when there is no filter in place. Direct
exposure of the cell to any light may damage the cathode.
3)
Do not look
directly at the mercury lamp. This may damage your eyes. As a precaution, block
the mercury lamp when it is not being used.
Improvement:
1) Use as less light for lamination as possible.
2)
Handle the equipment carefully. For example, do not touch the optical
part of the filter.
9.
Conclusion
The Planck’s constant and the work function are found to be 4.58 x 10-34 Js and 1.6 eV. The cut-off frequency is found to be 3.488 x 1014 Hz. Also photocurrent depends on the intensity of light.