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Electron Diffraction
WARNING - A 5000 volt power supply is used in this experiment. From the manual, "The
output is current limited to minimize danger to the user, but receiving a shock from the output
is an extremely painful experience and may be physically harmful. There is no way to protect
the user from the danger of the high voltage output of the supply. Your safety remains your
responsibility." In other words, have the instructor check your wiring before your turn on the
high voltage.
WARNING - These tubes are very expensive and somewhat easy to damage. After turning the
filament power on, wait a full minute before applying high voltage. In addition, keep a close eye
on the current. It should be kept below 0.2mA. The high voltage should be turned down between actual
measurements and measurement time should be minimized to protect the several-atomic-layer-thick
carbon film on the target.
In Louis de Broglie's doctoral thesis he posited that particles obey the same relationship bewteen
wavelength and momentum that photons do, namely λ = h/p. For a short time this prediction
was untested, as no one could find a diffraction grating small enough to observe the wave nature
of particles. Davisson and Germer's accidental diffraction results were followed by careful study that
supported de Broglie's theory. In today's lab we will make three measurements of h by observing the
diffraction of electrons by a thin carbon film.
The diffraction tubes are electron guns, just like traditional television tubes. A filament is
supplied with a current, and thermally excited electrons leave the metal. These electrons are
then swept up by the electric field created by a high voltage. If one assumes that the electrons
have essentially no velocity as they leave the filament, then by conservation of energy we can
write their final velocity as
v = (2 e V/m)0.5
Where e is the charge of the electron, m is its mass and V is the voltage applied to the tube. Once
the final velocity is known, one can solve for the wavelength:
λ = h / (2 e m V)0.5
The equation for diffraction is n λ = 2 d sin θ, where d is the lattice spacing of carbon,
but for first-order peaks and small angles this reduces to λ = 2 d θ.
When the electrons strike the carbon film they diffract into rings. They become rings rather than
points because of the random arrangement of the grains in the carbon film. There are two rings because there
are two atomic spacings in the carbon lattice. To measure θ we measure the
the diameter of the rings and use the following formula:
θ = D / (4 L)
Where D is the diameter of the rings and L is the distance from the carbon film to the screen - 13cm.
An important complication to note here is that the formula demands constant L, and since the globe
is curved this assumption is not valid. Much of this error is cancelled if one places a piece of
clear tape on the globe and makes marks on the tape corresponding to the positions of the rings. Once
the tape is peeled off and laid flat, a more accurated measurement can be made. Some people find
that is is easier to see the rings from the back of the globe rather than viewed from the front, and some
also find that measuring the edges and middle of the rings is better than just measuring the middles. Make
sure the tape is applied with no wrinkles.
Wire up the experiment as instructed by the professor. After inspection the filament current
should be turned on for a full minute. Slowly increase the high voltage; if the high voltage
is applied before the filament is warmed up, you may damage the tube. Raise the high voltage
until the rings are visible, and then continue to increase the voltage until you reach 4.0 kV.
Remember to keep the current below 0.2 mA (this may mean you can't get to 4.0 kV, in which case
you should go to 3.75 kV. You can go beyond 4.0 kV is your current stays low). Step down in
increments of 0.25 kV until you can no longer measure the
position of the rings. If you simply make marks on your tape, you can collect data quickly
and avoid damaging the equipment. Use calipers to measure the data from your tape.
The data in this experiment should be graphed with θ on the y axis and
V-1/2 on the x axis. The slopes of these two lines, along with some physical
constants, can be used to determine Planck's constant. The book values of the carbon lattice
spacings are 0.123nm and 0.213nm. Remember that you need to include error bars for
your final results. Write down which tube you use and include current as a function of voltage data as an appendix in your lab report. This allows
us to track the quality of the individual tubes.
Once you have completed measurements in this fashion, wait until another group has finished with their setup.
Trade lab stations and the place pieces of tape across the globe as before, but this time put ruler markings
on the tape. Turn up the voltage to the highest value that does not violate the current warnings and take a
photo with your cell phone. Turn down the voltage by 250V and repeat until it is hard to distinguish rings. Use
photo software to measure the diameter of each ring in pixels, and use these data as a second measurement for h.
Again, write down and report the tube you are using.
Students should also perform the online version,
which is an electron diffraction tube in Germany set up with a remotely-controlled high voltage source
and a webcam. Screenshots should be analyzed for data. Their tube is slightly different, so L=13.5cm.
Include analysis for these data in your lab report. Note that since only one person in the world can use it at a time,
it's a good idea to do this before lab.
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