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Transcript
Laboratory#3 – Phys4480/5480
Dr. Cristian Bahrim
Photoelectric effect
In 1900, Planck postulated that light is emitted and absorbed in discrete but tiny bundles
of energy, E = h ν , called today photons. Here h is the Planck’s constant 6.626 x 10-34 J.s and
ν is the frequency of the light. In 1905, Einstein did a step further and postulated that the light
propagates that way as well. So, actually light is a particle phenomenon. This was in
complete disagreement with the well-established wave theory for light demonstrated in various
experiments. In 1905, Einstein proposed a simple theoretical model able to explain the
photoelectric effect, a phenomenon that was recently discovered by Hertz. Einstein’s model
demonstrates clearly that light can be considered a stream of photons rather than a wave.
The photoelectric effect occurs when a metal surface is illuminated with light of
certain frequency and electrons are emitted by the surface. These electrons are usually
called photoelectrons. This phenomenon can be studied using the set-up shown in Fig. 1. An
evacuated tube contains two electrodes connected to a source of variable voltage. One
electrode is a metal plate positively charged (the anode). When light of certain frequency
irradiates the anode, kinetic electrons from the metal are emitted. The electric field between the
electrodes will decelerate these photoelectrons. However, some of the photoelectrons have
enough energy to reach the cathode despite its negative polarity, and they form a photocurrent.
The slower photoelectrons are repelled before they get to the cathode. When the voltage is
increased to a certain value no more photoelectrons arrive to cathode and the photocurrent
drops to zero. This extinction voltage (or stopping potential), Vs, corresponds to the maximum
kinetic energy of the photoelectrons (or the kinetic energy of the most energetic electrons), Kmax:
e Vs = Kmax
[1]
where e is the electronic charge.
Based on the principle of conservation of energy, Einstein proposed the following
equation in order to describe the photoelectric effect:
K max = hν − φ
[2]
where φ is the work function of the metal and represents the minimum energy needed by
an electron to escape the Coulomb attraction of the metal surface.
The experiments have shown that within the limits of experimental accuracy (about 10-9
sec), there is no time delay between the arrival of light at a metal surface and the emission of
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photoelectrons. [ The EM theory predicts a time delay of about 1 sec. between the moment
when the wavefront of light reaches the metal surface and the release of the photoelectrons.
This is because the absorption of the entire wavefront takes a certain time. ] Second, a bright
light yields more photoelectrons than a dim light of the same frequency, but the energy of the
electrons remains the same. [ The EM theory of light, on contrary predicts that more intense the
light, the greater the energies of the electrons ]. Finally, it was observed that larger the light’s
frequency, the more energy the photoelectrons have. Absorption of blue light results in faster
photoelectrons than of red light. Below a certain frequency, photoelectrons cannot be released
even if the source of light is extremely bright. None of the results can be explain by the wave
theory of EM radiation.
The experimental observations listed above follow directly from Einstein’s hypothesis:
(1) Because the light energy is concentrated in photons and not spread out, there should be
no delay in the emission of photoelectrons.
(2) All photons of frequency ν have the same energy, E = h ν . Therefore, changing the
intensity of a monochromatic light beam will change only the number of photoelectrons
and not their energy.
(3) The higher the frequency, the greater the photon energy and so, the more energy the
photoelectrons have.
In this experiment a photocell is irradiated with various monochromatic
radiations. You will use discharge tubes, various lasers and gas lamps.
You have to filter the light in order to select a certain wavelength. A
potential difference, V, is applied to the tube so that it opposes the energy
of the emitted photoelectrons. The voltage required to just stop the current
flow is proportional to the energy of the photoelectron. The minimum
detectable photocurrent is 5 x 10-10 A (or 0.5 nA).
GOAL: Plotting the stopping potential as a function of the reciprocal of the wavelength
of the radiation gives a straight line. From the slope you have to find the Planck’s
constant, h (the accepted value is 6.626 x 10-34 J.s), or better, the constant hc (the
accepted value is 1240 eV.nm).
e Vs =
hc
λ
−φ
[3]
Equation [3] is obtained by combining equations [1] and [2].
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Measurements and data analysis:
1. Alignment: Put the photocell in front of the source of light. Move the apparatus until the
radiation is striking the center of the photocell. Put the color filter indicated by the
instructor in front of the photocell in the holder. Make sure that most of the light goes
through filter (this is particularly important when an expanded laser beam is used).
2. Calibration: Set the zero of the photocell by turning the “Voltage” knob to a voltage high
enough to stop the current. For that turn the “voltage” knob all the way in the clockwise
direction. Adjust the “Zero” knob so that the meter reads exactly zero.
3. Turn the “Voltage” knob to its counterclockwise limit. The voltmeter should read zero
voltage. Now the photocell produces its maximum photocurrent. Adjust the distance
between the photocell and the source of light in such a way the photocurrent to be high
enough but within the scale.
4. Start reading the voltage from a high photocurrent (but not larger than 12 nA). Reduce
the photocurrent by increasing the voltage, until the current reaches zero. Write the
values for voltages for the current indicated in the Table 1. Be aware that in most of the
cases the photocurrent decreases to zero very slowly. So the reading of the voltage
near zero current should be done with maximum attention!
5. Using Excel, plot the photocurrent i versus the voltage V for three of the cases where the
range of photocurrents is very large so you can use many data points (eventually all 14
points). Show one plot with three curves. Check if the points follow a smooth curve.
Show the plot to your instructor.
For plotting follow the steps:
a. Open Microsoft Excel and fill out a spreadsheet with data. Consider VS the xvariable and i the y-variable.
b. Go on Insert, Chart. It will open the “Chart Wizard” window.
c. Select XY (Scatter) and smooth curve for “Chart Type” and click Next.
d. Select in “Data Range” the data for the electric current (highlight the column).
e. Click on “Series” and go to “Category (X) axis labels”. Select the data for the
stopping potential and press Next.
f.
Press Finish.
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6. In Table 2 you need to include the values of the energy associated to the stopping
potential, as well as of the reciprocal of the wavelength for all sources of light you have
investigated.
Table 2.
Stopping
Source of light
energy
λ (nm)
1/λ (nm-1)
eVs (eV)
Diode red laser
650
Red laser
633
Na-lamp
589
Green laser
544
Green diode laser
532
H-discharge
486
Blue diode laser
473
Hg-lamp
404.65
He-discharge
388.86
7. Make a linear regression of the data introduced in Table 2.
For linear regression follow the steps
a. Open Tools, Data Analysis, Regression.
b. A window called “Regression” will appear on the screen.
i. Go with the cursor on ”Input Y range” and next select the column of data
for the dependent variable. This should be the Stopping energy eVs (eV)
ii. Go with the cursor on ”Input X range” and next select the column of data
for the independent variable. This should be 1/λ (nm-1).
iii. Don’t set “Constant to zero” (according to Eq. [3], the intercept is -φ).
iv. Click on “Output range” and the empty cell next to it, and next, on the
spreadsheet in an empty cell.
v. Click OK.
c. You will get a report. Identify on the last line “X variable” the number below
“Coefficient”. This number is the slope (according to Eq. [3] is the constant hc).
4
8. Report the value for hc with an error bar (“The standard error”) and from the intercept the
work function φ (in eV) with an error bar (“The standard error”).
hc = (
±
) eV.nm
φ =(
±
) eV
You can also find the Planck’s constant in SI units:
h=
slope ∗ e
=
c
J.s
where e = 1.6 x 10-19 C and c = 3 x 108 m/s.
9. Compare the experimental value for hc with the theoretical value of 1240 eV.nm. Is the
accepted value included in the experimental interval? If yes, you have just proved that
the light is detected as a photon!
Studies:
#1. Using of a bad filter:
When you use the Hydrogen discharge, you need to filter the light
and select a wavelength. Because the most intense line of Hydrogen is at 656.2 nm, the logic
choice is to use a red filter. A good red filter is expected to eliminate all wavelengths below 580
nm. However, you will observe that this red filter leaves the blue light of wavelength 486.1 nm to
pass. You will find experimentally that the stopping potential you are measuring, corresponds to
a photocurrent produced by photons of 486.1 nm. You need to check that the new point for
Hydrogen @ 486.1 nm will be on the same linear trend Vs versus λ−1 that you can plot (on a
graph paper) using the data from Table 2..
Remark: The source of Hydrogen produces a very weak current!
#2.
When you use the Hg vapor, you can check that the value of the stopping voltage is
independent on the intensity of the light incident on the photocell. For that you can use a Hg
discharge tube instead of the Hg lamp. You will see that the intensity of the source of light
doesn’t change the energy of the most energetic photoelectrons. So the stopping voltage is the
same. The energy of the photoelectrons depends only on the light’s frequency and not its
intensity! This fact is in clear disagreement with the wave theory and it can be explained ONLY
by the photon theory.
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SETUP – PHOTOELECTRIC EFFECT
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