Physics 321 Fall 2000
The Frank Hertz Experiment
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The Frank-Hertz Experiment and Quantized Energy Levels
In this experiment electrons scattering off mercury or neon (depending on the apparatus you use)
atoms are shown to give up energy in discrete quanta, demonstrating the existence of quantum energy
levels for the mercury atom.
NOTE:
We have a simplified apparatus, based on the energy loss of electrons in Neon, rather than Hg. These
instructions do not fully reflect the change, so you will need to be careful as to whether the instructions apply to the
older Hg apparatus or the new Ne apparatus.
I. References
Mellissinos,
II. Theory
In the Frank-Hertz apparatus,
mercury is vaporized or neon is
present in a specially designed
vacuum tube, the atoms of the
vapor providing targets for a
scattering experiment. Electrons
are accelerated through the vapor
by an applied electric field. (In
the discussion below, read neon
or mercury wherever mercury is
noted. As soon as they have
enough energy, about 5 eV for
mercury, they excite the next
mercury atom they hit to its first
excited state. This is observed
as a drop in the current of
electrons passing through the
tube. Several such drops in the
beam current can be seen as the
acceleration voltage is increased,
corresponding to the electron
exciting one, two, three,...atoms during its passage through the tube. (Note: the conditions of the neon tube and
spectrum are such that only 3 drops may be seen. If one is fortunate, as many as six drops in current may be
observed in mercury.) The excitation energy can be determined from the spacing of the peaks.
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Physics 321 Fall 2000
The Frank Hertz Experiment
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The energy levels of the
mercury atom are shown in
figure 1 to the left. The
lowest level is the ground
state. The transition which
we observe is from the
ground state to one of the 3P
states. While the details of
how these energy levels
arise may not be clear to you
at the present time, the
quantized nature of the
transitions should be.
III. Procedure
Note: If one is doing the
Neon experiment, steps A-D
are ignored. One will follow
similar procedures, but there
is no oven to adjust, and the
meter one uses is the
laboratory digital multimeter, as the commercial apparatus has a built-in current amplifier for the electron current. In
fact, we will just look at the Neon spectra dynamically, on an oscilloscope.
A. The tube should be heated for a while before starting the experiment, preferably an hour or more. (Finding
the right temperature to see the minima clearly is the most challenging part of this experiment! The variac
should be set to 50 V (the higher of the two points marked). Put in 1.5-volt batteries for the two grid biases
G1 and G2. (See the circuit diagram of figure 2.) Please remember to remove the batteries at the end of
the session, or they will run down. Verify with a voltmeter that you can adjust G1 between 0 and +1.5 V
relative to the cathode (FC), and G2 between 0 and +1.5 V relative to ground. Set them both initially to
1.5 V.
B. Connect the Keithley electrometer. Connect the power supply from FC to G2 with G2 positive, and set it to
10 volts. You should measure a current of about 10 -6 A when the tube is cold, decreasing as it heats (why?
–Your thoughts or speculations on this should be in your book, as should other questions that arise in your
own mind. Don't be afraid to say something that is wrong. Rather, use the book to expand your thinking. )
to around 3x10-9 A when hot.
C. Note how the beam current depends on the G1 bias voltage. G1 acts like a valve, to turn the beam off and
on. You may find later on that smaller beam currents permit you to go to higher accelerating voltages
without the tube sparking off.
D. Sweep the accelerating voltage to a maximum of 40 V. Caution! A discharge may take place at some value
of this voltage, causing a jump in the anode current. If this happens, turn the voltage down at once.
E. Try to find a series of current troughs as you sweep the voltage. You may have to change the oven setting.
The tube can easily be cooled by pulling it part way out of the oven. The general effect of raising the
temperature is to accentuated the high-voltage troughs; cooling enhances the low-voltage troughs, but often
loses some of the high-voltage troughs. But with this experiment, there are no fixed rules. What works best
with one set-up may not work well at all with another.
F. From part E. you should have an idea where the troughs are, and what the range of current you expect. Make
a labeled set of axis in your laboratory book, and record current vs. accelerating voltage. The loss of
energy experienced by the electrons when they excite the atoms will occur over a range. It is not really
clear where the optimum point is to measure. Fluctuation in the heater voltage due to the IR drop as a
function of position, for instance, adds a range of values of maximum energies of the electrons. Your
objective is to measure the difference between corresponding parts of the absorption from minima to
minima. You may wish to try two alternatives, 1) measurement of the position of the half height of the
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Physics 321 Fall 2000
The Frank Hertz Experiment
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drop from just before the current drops to the minimum or 2) measurement of the bottom of each trough.
To do either, you need detailed readings from the peak through the trough, and not at all detailed when you
are not at a trough. For instance, if you measure the difference between trough minima, you will want to
obtain data on either side of the minimum, and find the minimum as the average between corresponding
points on the sides of the trough. Similarly, if you use the half-way down of the initial slope, you will want
data at the peak and at the trough in order to estimate the location of the 1/2 height point. (With the Hg
vapor tube, if you spend time taking data away from the troughs, you may find that the whole curve has
shifted by the time you finish due to the changing temperature, and you will only obtain a lot of frustration.)
When you mark the point on your graph, you can also record the values measured next to the point so that
you do not lose any significant figures on the graph.
Do a linear fit to determine the excitation energy and its error. The y-coordinate should be voltage, and the
x-coordinate, peak number. The resulting slope determined by the fitting program is the peak spacing, in
volts. Compare with values which will be supplied by the instructor.
IV. Equipment
Frank-Hertz apparatus
laboratory digital voltmeter
(For old Hg apparatus:
Keithley 610-C electrometer
40-V power supply)
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