Download The Photoelectric Effect

The Photoelectric Effect
R.L.Griffith,M.R.Levi,D.Cartano
ABSTRACT
According to the photon theory of light, the maximum kinetic energy, KEmax , of photoelectrons depends only on the frequency of the light, and is independent of the intensity. In
contrast, the classical wave model of light predicted that KEmax would depend on light intensity. A PASCO scientific h/e apparatus was used to study the photon theory of light versus
the wave theory of light. The apparatus was used in combination with the PASCO mercury
vapor light source. The light was than placed incident onto a special fluorescent material and
the stopping potential was measured with a standard volt meter. With the stopping potential
measured we are able to to make a plot and acquire the slope of the line, with the slope we
are able to calculate the experimental value for h, planck’s constant and compare it to the
theoretical value. The work function φ will also be acquired and compared to the theoretical
value. The wave theory of light will also be tested by changing the intensity of the light that is
incident on the special fluorescent material, to determine if the stopping potential is independent of the intensity of light. We acquired 1.52(first order) and 13.87(second order) percent
error for the trial on the relationship between energy, wavelength, and frequency. We acquired
3.05(first order) and 14.16(second order) percent error for the work function.
Subject headings: Electromagnetic wave-particle duality, photoelectric effect
1.
Introduction
photoelectric effect in his quantum model using
Upon exposing a metallic surface to electromagnetic radiation that is above the threshold
frequency, the photons are absorbed and current
is produced. No electrons are emitted for radiation with a frequency below that of the threshold. By conservation of energy, the energy of the
photon is absorbed by the electron and, if sufficient, the electron can escape from the material
with a finite kinetic energy. A single photon can
only eject a single electron, as the energy of one
photon may only be absorbed by one electron.
The electrons that are emitted are often termed
photoelectrons. In 1901 Max Planck proposed
his law of radiation, which stated that an oscillator has discrete set of possible energy values. The energy lost or gained by the oscillator
is emitted or absorbed as a quantum of radiant
energy, the magnitude is expressed by the equation
E = hf
E = hf = KEmax + φ
(2)
where KEmax is the maximum kinetic energy of
the photon and φ is the work function of the
material. Relating the kinetic energy with the
stopping potential yields
KEmax = eV
(3)
where e is the charge of one electron which is
1.602 × 10−19 and V is the stopping potential.
Therefore, using Einstein’s equation
hf = V e + φ
(4)
when solve for the stopping potential, the equation becomes
µ ¶
µ ¶
φ
h
f−
V =
e
e
(1)
(5)
³ ´
¡ ¢
where he is the slope of the line and φe is the
y intercept. From these two values we are able
to determine the accuracy of this experiment.
where E is the energy, h is planck’s constant
which is 6.626 × 10−34 J · S, and f is the frequency of the electromagnetic radiation. Einstein applied Planck’s theory and explained the
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2.
2.1.
Method
Spectral line
Color
Yellow
Green
Blue
Violet
Ultra Violet
Model
SE-9589
AP-9368
OS-9286
AP-9369
Procedure
This experiment consisted of two different trials. The first part is performed investigates the
maximum energy of the photoelectrons by relating it to the intensity of the light. The yellow
spectral line was used with a transmission filter.
The transmission filter was used to regulate the
intensity of the incident light upon the detector
and the stopping potential was measured. The
second part of this experiment investigates the
maximum energy of photoelectrons as a function
of frequency of the light. The different spectral
lines were incident on the detector at 100 percent
intensity and the stopping potential was measured. A complete description of the procedure
can be found in the Los Angeles City College
Physics 103 lab manual.
3.
Data and Calculations
First order spectral line
wave length frequency stopping potential
nm
x1014 Hz
volts
578
5.18672
.711
546.074
5.48996
.847
435.835
6.87858
1.477
404.656
7.40858
1.705
365.483
8.20264
1.918
Second order spectral line
Yellow
578
5.18672
.643
Green
546.074
5.48996
.718
Blue
435.835
6.87858
1.287
Violet
404.656
7.40858
1.448
Ultra Violet
365.483
8.20264
1.663
Measured quantities
Equipment Used
Equipment
Digital voltmeter
h/e Apparatus
Mercury vapor light source
h/e Apparatus accessory kit
2.2.
3.1.
Fig. 1.— frequency vs. stopping potential, first
order.
Results and Discussion
The frequency and the wavelength of each
color is acquired using table in Fig. 10 on page
six of the lab manual. They are the same for the
first order and second order measurements. The
slope and y intercept were acquired using IDL’s
linear fit routine LINFIT. From equation 5 and
knowing the slope of the line, the experimental
value for Planck’s constant h can be measured.
Also from equation 5 we are able to determine
the work function φ for the material, comparing
the experimental values to theoretical values we
are able to determine the error in this experiment. The wave vs. quantum model was also
tested using a variable transmission filter. The
yellow spectral line was used for this trial, the
time required for the volt meter to return to the
original recorded voltage was measured to prove
Planck’s hypothesis. A summary of the data is
given in the following tables.
Fig. 2.— frequency vs. stopping potential, second order.
2
Graph
first
second
Graph
first
second
Graph
first
second
Graph
first
second
Analysis
4.
Calculation for h
e(Coulumbs)
Slope
1.602 × 10−19 4.199 × 10−15
1.602 × 10−19 3.563 × 10−15
Error Measurement
Theory(J · s)
Exp.(J · s)
6.626 × 10−34 6.727 × 10−34
6.626 × 10−34 5.707 × 10−34
Work Function φ
y-intercept(y)
φ = e(y)(J)
-1.455
2.331 × 10−19
-1.212
1.942 × 10−19
Error Measurement
Theory(eV)
Exp.(eV)
1.412
1.455
1.412
1.212
h = e × slope
6.727 × 10−34
5.708 × 10−34
% error
1.52
13.87
φ (eV)
1.455
1.212
% Error
3.05
14.16
Conclusion
This lab was conducted to test Planck’s quantum model to the wave model of electromagnetic waves. The first trial was conducted to test
wether the intensity of light affected the KEmax .
The classical wave model of light predicted that
KEmax would depend on light intensity. The
observed outcome showed that this was not true
and that the quantum model is the correct model
to use. We observed that changing the intensity
with a Variable transmission filter, only affected
the time it took to reach the required stopping
potential. The second trial was conducted to test
how the change in frequency of the light affected
the stopping potential of the photoelectrons. We
observed that as the frequency increased, the
stopping potential also increased, and that the
frequency is proportional to the stopping potential, as stated in equation 5. The errors acquired showed that Planck’s quantum model can
be used to predict the behavior of photon energy
and their effects on photoelectrons. The possible explanation for the amount of time it took to
reach the required stopping potential in the first
trial can be explained by the probability that
a photon(of appropriate energy) made contact
with an electron was a lot smaller for lower intensity light than it was for the higher intensity
light. Based on our lab results this experiment
supports the quantum model of light and is in
opposition to the classical wave model.
REFERENCES
Los Angeles City College Lab Manual Physics
103.
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