Download Photoelectric Effect

Photoelectric Effect
Introduction
The photo cell is used to demonstrate the photoelectric effect. When the photocathode is irradiated with light,
electrons are liberated from the photocathode and can be detected at the anode ring as a photoelectric
current in a suitable circuit. This device can be used to show that the energy of the light is proportional to the
frequency of the radiation and independent of the intensity of the radiation. When the photocathode is
irradiated with monochromatic light, it is possible to determine Planck’s constant. In addition to confirming
Planck’s calculations for the radiation of a black body, Einstein’s interpretation of these experiments
confirmed the quantum nature of light.
Functional principle
•
Light is emitted by a high pressure Mercury lamp.
•
Several lenses focuses the light beam towards the
photocell
•
Interference filters can be used to select a special
wavelength
•
Inside the photocell the light causes the emission of
electrons at the cathode through photoelectric effect.
•
The electrons fly to the circular anode which rise the voltage in the capacitor and the anode. This
ends up in an electric field between anode and cathode so that the electrons were slowed down
since they are no longer able to reach the anode. The voltage between anode and cathode is a
measurement for the energy of the electrons.
•
The whole configuration is placed in a vacuum tube to avoid collisions between electrons and gas
molecules of the air.
Interference filters
Cathode
Circular anode
High pressure
Mercury lamp
U0
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Photoelectric Effect
Setup
Equipment
Assembling the experiment
•
1 Photo cell
1. Connect the universal choke to the mains via the distribution
•
1 Basic device for photo cell
•
1 High pressure mercury lamp
box.
2. Mount the high-pressure mercury lamp (a) at the marked
•
1 Universal choke, in housing,
230 V, 50 Hz .
•
1 Lens in holder, f = + 100 mm
•
1 Iris diaphragm in holder
•
1 Filter revolver with several
interference filters
•
1 Electrometer amplifier
•
1 Plug-in unit 230 V AC/12 V AC
•
1 STE capacitor, 100 pF, 630 V
•
1 STE key switch (N.O.)
•
1 Voltmeter, DC
•
1 Optical bench with standard
profile, 1 m
•
Cables
position using an optical rider (H = 90 mm), connect it to the
universal choke and switch it on.
3. Mount the photocell (e) at the marked position using an
optical rider (H = 90 mm); remove the cover and align the
photocell so that the coated black surface is facing the
mercury lamp. Do not attach the cover yet.
4. Mount the iris diaphragm (b) on the optical bench at the
marked position using an optical rider (H = 120 mm).
5. Mount the lens (c) at the marked position using an optical
rider (H = 120 mm), revolve the filter holder so that there is no
filter in the lightray.
6. Mount the filter revolver with interference filter (d) at the
marked position using an optical rider
7. Adjust the heights so that the center of the lens and all other
equipment is at the same height as the center of the iris
diaphragm.
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Photoelectric Effect
8. Set up the electrometer amplifier circuit as shown in the figure
below.
9. Attach terminal plug (f) and connect the 100 pF capacitor and
the key switch.
10. Attach coupling plug (g), the BNC/4 mm adapter and the
straight BNC and connect these to the gray screened cable of
the photocell.
11. Connect both black cables (h) of the photocell to the ground
connection on the electrometer amplifier.
12. Connect the multimeter to the output of the electrometer
amplifier.
13. Connect the plug-in supply unit (12 V) to the electrometer
amplifier and plug it in via the distribution box.
14. Connect the optical bench (and possibly the rod of the basic
device of the photocell) to the ground connection of the
electrometer amplifier, and connect this terminal to the
external ground of the distribution box.
Experimental procedure
1. Switch on the multimeter and set the range switch to 1
V DC.
2. Turn the interference filter for yellow light ( λ = 578 nm)
into the beam path.
3. Discharge the capacitor by holding down the key switch
until the multimeter reads zero V.
4. Start the measurement by releasing the key switch; wait
about 30 s to 1 minute, until the capacitor has charged
to the limit voltage U0. Write down the measured value
for U0 in a table like the one below.
5. Turn the interference filter for green light ( λ = 546 nm)
into the beam path and repeat the measurement.
Safety precautions
•
•
The high pressure mercury lamp also emits light in the UV range, and can thus
damage the eyes. Never look into the direct or reflected beam of light from the high
pressure mercury lamp.
!
Do not exert mechanical force on the vacuum cell, danger of implosions!
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CERN Teachers Lab
Photoelectric Effect
Photoelectric effect
Tasks:
1. Measure the limit voltage U0 for violet (λ=405 nm) and yellow (λ=578 nm) light. What differences can
be found?
2. How does the limit voltage change if you increase the intensity of the light?
Results:
1. The limit voltage U0 is much bigger for violet than for yellow light.
2. The intensity of the light does not influence the limit voltage.
With classical wave theory of light we would expect that the emission of electrons does not depend
on the wavelength of the light. The photoelectric effect (and the limit voltage U0) should depend on
the intensity, not on the frequency or wavelength of light. How we saw in this experiment, this is not
true: the limit voltage is proportional to the wavelength and not to the intensity.
The explanation for this phenomenon was given by Einstein in 1905:
he postulated that light consists of a flux of particles, called photons,
whose energy E is proportional to the frequency ν:
E = h ⋅ν
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(h = 6,62*10 Js: Planck’s constant)
The irradiated photons may then “hit” an electron in the metal and, if
the energy is greater than the ionization energy W of the atom, make
the electron exit the atom.
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Photoelectric Effect
Determination of h/e und ionization energy W
Tasks:
1. Measure the limit voltage U0 for different wavelengths as described above and fill in the table:
Color
λ (nm)
ν (THz)
Yellow
578
519
Green
546
549
Blue
436
688
Violet
405
741
U0 (V)
2. Plot the measurements in a coordinate system with frequency (ν) on the first axis, and voltage (U0)
on the second, and make a best fit of a straight line trough the points (and/or by linear regression
h
analysis of the measurements) and calculate the slope of the line to determine /e und the ionization
energy W of the material of the cathode!
If the photons energy E = h ⋅ν is greater than the ionization energy W, the rest is found as kinetic
energy (Ek) of the electron (the photon “disappears”):
Ephoton = W + Ek ⇔ hν = W + Ek
Since the ionization energy of the atom is a constant, we can calculate Plancks constant h by
measuring the kinetic energy
Ek of the ejecting electrons. We use a photocell with an anode which
is used to slow down the electrons which are ejected when we illuminate the cathode layer with
monochromatic light. The anode voltage is made by charging a capacitor with the ejecting electrons.
The voltage in the capacitor will then rise until the ejecting electrons are no longer able to reach the
anode – then we know that the electric potential between the anode and cathode is exactly equal to
the kinetic energy. The work done on a charge that falls trough a electric potential U is given by
EU = eU (e is the charge of the elecrons – the elementary charge). We measure this voltage and
wait until it reaches the limit voltage
electrons. Then we can set
U 0 , which then gives us a measure of the kinetic energy of the
Ek = eU 0 in the above equation:
hν = W + Ek ⇔ hν = W + eU 0
We then are able to express this voltage as a linear function of frequency of the light:
hν = W + eU 0
eU 0 = hν − W
h
W
U0 = ν −
e
e
This is a linear function with slope
h
, so that if we measure the voltage for light with different
e
frequency and find the slope of the best-fit straight line trough these points, we can multiply this by
e = 1.6 ⋅ 10 −19 C and get an estimate for Planck’s constant.
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Photoelectric Effect
Results:
1. Values:
Color
λ (nm)
ν (THz)
U0 (V)
Yellow
578
519
0,66
Green
546
549
0,76
Blue
436
688
1,35
Violet
405
741
1,53
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2. The quotient of Planck’s constant (h=6,62*10 Js) und elementary charge (e=1,6*10
h
-15 Js
/e=4,14*10
/C. The ionisation energy of the photocathode is W=1,4274 eV.
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C) is:
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