Download PHOTOELECTRIC EFFECT Introduction

PHOTOELECTRIC EFFECT
Light : wave or quanta? Measurement of Planck’s constant.
Introduction
Is light a continuous wave, or is it quantized in energy and space, or can it be one and the other?
By observing what occurs when various wavelengths and intensities of light shine on metal, you
will be able to better understand the nature of light. You also need to obtain an experimental
value for Planck’s constant, the fundamental constant of quantized systems.
Theory
When light shines on a clean metal surface, electrons may be ejected. This occurs only when
the electrons in the metal absorb a sufficient amount of energy from the light to escape from the
metal. This energy is called the binding energy or work function Φ. The work function is different for each type of metal. Energy absorbed in excess of this binding energy is carried off by the
electron as kinetic energy. Some of this kinetic energy may be transferred to other electrons or
atoms in the metal so that the electrons will have a range of kinetic energies leaving the metal.
Consider the following theories:
• Theory 1 -Classical Electromagnetism
Classical wave theory states that when light energy is absorbed by electrons, energy is
transferred continuously. After an electron has absorbed sufficient energy Φ, it will leave
the metal with a minimum of kinetic energy. Increasing the light intensity (electromagnetic
energy per second per unit area) causes electrons to leave the metal at a greater rate and
attain greater kinetic energy. Increasing the frequency while maintaining light intensity
does not change the rate of electron emission. Any frequency of light will eject electrons
if sufficient intensity and time is provided.
• Theory 2 -Light as Quanta
Quantum theory claims that the energy of light is concentrated into discrete bundles called
photons. For a given wavelength of light, each photon has the same energy
E = hf = hc/λ
(1)
where h is a constant, f is the frequency of the light, c is the speed of light, and λ its
wavelength. The intensity of light determines the rate of electron emission from the metal
provided that each photon has sufficient energy to eject an electron. Light of sufficiently
high frequency f ejects electrons even at very low intensities.
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Apparatus
The photoelectric effect circuit consists of a photo tube, a potentiometer, a 3 − 15V DC power
supply, an electrometer, and a voltmeter (see Fig. 1).
anode
cathode
A electrometer
voltmeter
V
+
−
Figure 1: Photoelectric effect schematic
Light Sources and Filters
Light from various types of light sources can be used to produce electron emissions. However
only the frequency and the intensity of the used light is important. Typical light-sources for this
experiment are : Mercury arc, Sodium arc, and Helium Neon laser.
We will only use a Mercury arc light source. The wavelength is narrowed using light filters. The
intensity is adjusted using a diaphragm.
Phototube
The phototube consists of a cathode which is a metal plate with a low work function Φ, and
an anode. When light strikes the cathode, electrons are ejected with a range of energies. Some
electrons will reach the anode and be measured as a small current by the electrometer. Light can
also produce photo emission of electrons from the anode. This effect is reduced by making the
anode small and shielding it from the light. Electrons lacking adequate kinetic energy to reach
the anode will eventually return to the cathode.
Electrometer
Measure the photo current with an electrometer. This sensitive device measures picoamperes
(10−12 amperes) of current. To read the electrometer, multiply the needle position by the sensitivity selected. Use a coaxial cable to place the electrometer in series with the photocurrent.
Current flows into the electrometer through the inner conductor of the coaxial cable and out
through the outer cable. The polarity (the direction the current is flowing) can be seen by a plus
or minus sign at the front of the electrometer (the needle will always be at positive values).
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Stopping Potential
Vary the photocurrent by applying a negative potential V to the anode. Measure this potential
with a voltmeter placed parallel to the voltage source. This potential decelerates the electrons,
converting their kinetic energy to electrostatic potential energy. Assuming that theory 2 is valid,
no electrons will reach the anode when
hf − Φ = eVs
(2)
Vs is called the stopping potential and e is the electron charge. If V exceeds Vs , no electrons
will reach the anode, and the current will be zero. Further increase of V will cause a (very
small) current in opposite direction, due to electrons leaving the anode. While it is impossible
to totally suppress electron emission at the anode, (direct) light striking the anode will produce a
lot of electron emission. Because the anode is held at a negative potential relative to that of the
cathode, emission from an unshielded (unprotected) anode would subtract significantly from the
photocurrent. That is why the anode is a ring wire, which must not be illuminated by direct light
from the light source. Furthermore it is advisable to minimize the amount of light in the vicinity
of the experiment (darken room).
The approximate behavior predicted by each theory is shown in Figure 2. Note that the voltage
axes are negative.
I = intensity , I1 > I2 > I3
a)
b)
c)
current
current
I1
I3
I2
I1
− voltage
I2
−Vs
I3
− voltage
/h
frequency f
Figure 2: Theory 1(a) and Theory 2(b,c) Predictions
(a) a plot of photocurrent vs. applied voltage. Frequency and time are fixed.
(b) A graph of photocurrent vs. applied voltage. Frequency is fixed and time is independent.
(c) A plot of stopping potential vs. frequency. Intensity is fixed and time is independent.
If theory 1 is valid, the current will decrease to zero as you increase Vs ; also, this stopping
potential will be roughly proportional to the light intensity.
If theory 2 holds, equation 2 should give the relationship between Vs and f . The stopping
potential will be the same regardless of intensity. To check these hypotheses use bandpass filters
and vary the amount of light coming from the light source. Bandpass filters allow only a narrow
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range of wavelengths to pass, whereas reducing the total amount of light reduces all wavelengths
by the same factor.
Procedure
Equipment Needed
• photoelectric effect apparatus
• mercury arc lamp
• lens
• color filter
• cable
• voltmeter (multimeter)
• electrometer
• power supply (0 − 15V )
• potentiometer
Step by Step
Connections
Connect the photoelectric effect apparatus to the power supply, the potentiometer, the volt- and
the electrometer as shown in fig.1. Put the electrometer into a ‘non-sensitive’ region. Before
switching on any of the devices, ask your tutor to check the setup.
Power Up
Turn the light source on and allow it a few minutes to reach operating temperature.
————————————————————————————–
CAUTION: Avoid looking directly at the mercury light source!
The intense ultraviolet rays can damage your eyes.
————————————————————————————–
Switch on the electrometer and the voltmeter. Be sure the batteries are OK (no warning on the
display!). Switch on the power supply and set it to about 5V . Set retarding potential to 0 by
using the potentiometer.
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Preparation
Insert the green filter in the holder in front of the source. Open the photoelectric effect apparatus
and adjust the position of the lens and apparatus itself so that a small, focused point of light is
seen on the photocathode. The anode must not be illuminated. Increase the sensitivity of the
electrometer until it gives a clear signal. Do not pin the needle!
As you increase the retarding potential V , note that the current steadily decreases. This suggests
that the electrons indeed have a range of kinetic energies due to scattering in the metal.
Increase-decrease the amount of light coming from the lamp by tuning the diaphragm.
Note that the amount of emitted electrons, e.g. the photocurrent, indeed is a function of the
amount of light offered, as we had concluded from classic theory (Theory 1).
Measurements
• Increase the retarding voltage starting at zero until the photocurrent changes polarity. For
about 15 values of V measure the value of I. It is advisable to also take a few points
beyond the voltage where polarity switches. Do these measurement with all the filters.
• Change to the blue filter. As before measure the I(V ) values, but this time for increased/decreased
amount of offered light.
Analysis
1. Plot I versus V for each filter and determine values for Vs if they exist. Plot the data from
different intensities of blue light on the same graph. Does this graph support theory 1 or
2? Explain.
2. Plot Vs versus frequency f (f = c/λ). Does this plot support theory 1 or 2? Explain this
in terms of the plots in Figure 2 and the physics behind them.
3. If there is support for theory 2, use equation (2) to calculate Planck’s constant h from
the slope of your graph, and compare with the accepted value of 6.63 × 10−34 J/s. Note
that this is not a high precision measurement, as the choice of cutoff voltage is somewhat
subjective. Be impressed that you can measure such a small number at all.
Questions
1. What is the meaning of the f -intercept in your Vs versus f plot?
2. Estimate the work function of the cathode metal and compare with the expected value of
2.24eV . Experimental values may differ due to construction of the tube. A contact potential in the cathode-anode circuit inside the tube (photocell) adds to the applied potential
V.
3. Why should you be concerned about the scattered light reaching the cathode?
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4. Work functions of Tungsten (W ), Nickel (N i), Potassium (K), Iron (F e), Aluminum (Al),
and Platinum (P t) are listed below. Calculate the threshold wavelength for photoemission
of each.
W : 4.50eV
F e : 4.50eV
N i : 5.10eV
Al : 4.08eV
K : 2.24eV
P t : 6.35eV
5. Which of the above materials would you use for a high-vacuum commercial photoelectric
cell? Such cells must produce a photocurrent over as great a range of wavelengths as
possible. Explain your choice.
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