PLANK’S CONSTANT / PHOTOELECTRIC EFFECT
Ken Cheney
March 5, 2006
ABSTRACT
Plank’s constant will be measured using the photoelectric effect. The energy
per emitted electron is measured for several wavelengths of light, the data is
then fitted to Einstein’s equation E=H+hf or E=H+hv giving Plank’s
constant h and work function H.
INTRODUCTION
This experiment is of interest both because it measures one of the
fundamental physical constants, Plank’s Constant, and because it was the
second step in realizing that light could act like a particle, a photon.
In 1905 Einstein (in his spare time from inventing Relativity and calculating
the first observable effects of individual molecules – Browning motion)
showed that the photoelectric effect, which had been quite
incomprehensible, was easily explained if light consisted of photons
(modern name) of the energy given by Plank’s equation E=hf=hv.
DESCRIPTION OF THE PHOTOELECTRIC EFFECT- PROBLEMS
AND THE SOLUTION
It is observed that if light strikes a metal surface electrons are omitted – the
“photoelectric effect”.
1. More intense light results in more electrons.
2. If the light is of constant color the electrons are of constant energy.
Shorter wavelength light results in higher energy electrons even if the
intensity is constant or decreases.
3. Dim light still sometimes results in immediate emission of electrons.
The ultimate number of electrons is still proportional to the intensity.
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Problems if light is considered a wave (light obviously was and is a wave,
interference, diffraction, . . .):
In this picture light caries energy into the metal, heats the metal up
locally, and thermal electrons escape from the metal.
1. More intense light should heat up the metal more releasing faster
electrons – not observed!!
2. The heating (and hence the energy of the freed electrons) should only
depend on the intensity of the light – not observed!!
3. Dim light will always take a long time to produce enough heating to
release electrons – not observed!!
Einstein’s explanation, considering light as consisting of photons of energy
hf or hv:
Each photon struck an electron, giving the electron an energy proportional to
the energy of the photon. Then:
1. More intense light meant more photons, hence more electrons –
observed.
2. Short wave length (high frequency) photons would give the electrons
more energy – observed.
3. Even in dim light (few photons) sometimes a photon would arrive at
once and release an electron – observed!
EQUATIONS AND VARIABLES
Einstein’s photoelectric equation
E=H+hf=H+hv
E= the energy of the electron released from the metal by the photon
h=Plank’s Constant
f=frequency of light, common in textbooks now
v=frequency of light, traditional, Greek nu
H=Work function, the energy it takes to remove an electron from the metal
Electron energy in Joules = electron charge x voltage
Electron energy in electron volts, ev = voltage (1ev/1v)
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Plank’s energy equation (he didn’t visualize photons, just that the energy of
light was quantized – came only in steps)
Photon energy=hf=hv
METHOD
Known light frequencies are obtained by using lasers, Na light, and Hg
spectra.
The spectra are neatly produced by Pasco’s Na or Hg light sources, slit, and
lens / diffraction grating combination.
The photoelectric effect occurs inside a traditional vacuum tube photocell.
The photocell has a cylindrical metal plate (cathode) where the photons
release electrons. More or less at the center of curvature of the metal plate is
a wire (anode) to collect the electrons.
Electrons keep accumulating on the wire making it more and more negative
until no electrons from the metal source have enough energy to overcome
the repulsion from the electrons on the wire.
Ideally now you just connect a voltmeter between the cathode and anode and
measure the voltage. The energy of the most energetic electrons is given by
electron energy = Voltage x Electron Charge.
THINGS TO CHECK
1. PLANK’S CONSTANT
Find the maximum voltage for as many colors of light as possible.
2. IS THE ELECTRON ENERGY INDEPENDENT OF
INTENSITY?
Find the maximum electron energy for intensities of 100% to 10 % at
one color. You will use different neutral densities filters to check this.
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These filters let all colors through equally but reduce the intensity by the
given percent. Expect to find a small intensity dependence because of
charge leakage being more significant for low intensity light; therefore you
will never reach the maximum voltage with low intensity light.
EXPERIMENTAL FINE POINTS
Tape:
If photons strike the wire (anode) electrons will be knocked off. This will
prevent the anode from reaching the correct voltage.
There is a strip of (perhaps) tape on the side of the photocell to shield the
anode from photons.
Be sure that this tape does not block the light beam; the light has to strike the
cathode!
Amplifier:
Inside the same “black box” with the photocell there is also an “amplifier”
which does not amplify! What this “amplifier” does do is provide a very
high resistance where it is connected between the cathode and anode. The
current produced by the light is very small so even a small current through
the voltmeter can prevent the anode from reaching the proper final voltage.
Do remember to use the “zero” button to discharge the wire before each
measurement.
At low light intensities don’t expect to reach the maximum voltage.
At low light intensities expect to wait longer before reaching the maximum
voltage.
When possible use the colored filters to decrease the effect of stray light.
Light shield and UV converter:
In front of the photocell is a black cylindrical light shield, at the outside of
this light shield is a white plate with a slit for the light. The white plate lets
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you see the spectra to each side of the slit. In addition the white plate will
convert some ultraviolet light to visible light so you can see where the uv is.
ANALYSIS – PLANK’S CONSTANT
Plot the electron energy verses light frequency.
Do a least squares curve fit (regression) to Einstein’s equation:
E=H+hf=H+hv
This will give you values for Plank’s Constant, the work function, and R2.
Find the class average for Plank’s Constant and its standard deviation of the
mean.
ANALYSIS – INTENSITY VERSIS ELECTRON ENERGY
Plot the intensity (Percent transmitted) versus the electron energy.
Is the plot reasonably flat? Does it slope the correct direction?
DISCUSSION
 Are your results reasonably closest to the accepted value of Plank’s
Constant? What numerical evidence do you have to support your
opinion??
 Do you have a reasonable value for the work function?
 Considering the standard deviation of the mean, is the class average
reasonable close to the accepted value of Plank’s Constant?
 What could be done better??
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Photons
Phototube
Wire Anode
Metal
Cathode
Electrons
Electrons
Shield, tape
Glass Tube
Photo Detector
Circuit
1:1 Amp
High
Resistance Amplifier
High Resistance
V
Discharge
Switch
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