Download Laboratory #12: Franck-Hertz Experiment: Electron Spectroscopy

INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY
Laboratory #12: Franck-Hertz Experiment: Electron Spectroscopy
Goal: Verify Bohr's hypothesis that atomic excitation energies are quantized by repeating an
experiment which was first carried out by J.Franck and G.Hertz (Verband Deutscher Physikalischer
Gesellschaften, 16 (1914) 457), 12 years before quantum mechanics was developed.
Equipment: Franck-Hertz tube, oven, thermostat (NEVA), power supply -50V DC, 6.3V AC (NEVA
mains rect.), electrometer (Keithley 414A), variable 15Ω resistor, variable battery supply, 100:1
voltage divider, 2 instrumentation amps (Vernier), LabPro Box (Vernier).
(A)
The physics
Vo
ΔV
Figure 1
Electrons are ejected from a heated cathode and accelerated toward a grid that is at a positive
potential Vo relative to the cathode. Some electrons pass through the grid and reach the plate, which
is kept at a slightly lower potential Vp=Vo – ΔV. The current due to the electrons which reach the plate
is measured by a picoAmmeter. The tube is filled with mercury vapor. The Hg density depends on the
tube temperature. The density can be calculated from the pressure p that is given by the law of
Clausius-Clapeyron:
log p = − A / T + B + C ⋅ log T
(1)
Here, the vapor pressure p is in Torr, the temperature in K, the logarithm is to base 10, and the
values of the constants are A=3332.7, B=10.5457, and C=-0.848.
An electron traveling from the cathode to the grid collides with Hg atoms. The mean free path λ
between collisions is
(2)
λ = 1 /( 2 ⋅ π ⋅ n ⋅ R02 )
where Ro=1.5 10-10 m is the radius of the mercury atom and n is the number of atoms per unit volume.
At the end of one mean free path, the electron has gained a kinetic energy K from the electric field E,
where
(3)
K = eEλ
where e is the electron charge and E is the electric field established by the accelerating voltage Vo.
The loss of energy of an electron when it collides elastically with a Hg atom is greatest for a head-on
collision. One can show that this is still very small (see question below). If, however, the accelerating
voltage is large enough, some of the electrons may excite Hg atoms from the ground state to any of
the 3P excited states (see the Hg energy level diagram in fig.2). An electron that makes such a
collision has to give up the corresponding amount of energy, it then does not have sufficient energy to
overcome the opposing potential ΔV, and thus, it cannot reach the plate.
Initially, as the accelerating potential Vo is increased, the plate current rises until some of the
electrons can excite Hg atoms. At this point the plate current starts to decrease. After a minimum is
reached, further increase of Vo gives again a current rise until electrons can initiate an excitation
twice. Then, a similar drop in current occurs. With increasing Vo, this repeats many times. The
maxima are spaced by the 3Po excitation energy, E1 of Hg. The first maximum is not at E1 because of
the additional work required to extract electrons from the cathode surface. Excitation of states other
than the first is in principle possible, and you should look for them when you do the experiment.
Questions:
Calculate the Hg density for 180oC (453K) and 220oC (493K).
For the two temperatures, calculate the electron mean free path and the energy at the end of
the mean free path.
Calculate the fractional loss of kinetic energy in a head-on collision with a Hg atom.
(B)
Experiment:
Plug in the oven box heater. It takes about 20 min for the temperature of the tube to reach the
operating point of 170oC to 190oC. The thermostat adjustment is on the right side of the box. Also turn
on the picoammeter; it takes time to warm up, too. Check, sketch, and understand the wiring of the
setup; refer to figures 3 and 4. Add meters to measure Vo and ΔV. Set the retarding potential ΔV to
1.4V. Set the accelerating voltage Vo to the maximum of about 70V and adjust the AC filament
current with the 15Ω variable resistor such that the plate current reaches about 0.8 – 0.9 nA. Start the
Vernier Logger Pro software and configure CH1 and CH2 as “Instrumentation Amplifiers”. Setup the
plot to display potential 1 (Vo) on the X axis and potential 2 (plate current) on the Y axis. Configure
the LabPro software for a time-based measurement for 100 seconds and 10 samples/sec. Return the
accelerating voltage to 0 and start the data collection. Measure the plate current as a function of the
acceleration Vo by slowly and smoothly turning the voltage adjustment knob on the “Mains Rectifier”
from the lowest to the highest setting; this should take about 30 seconds. Stop the data collection and
save your data. Repeat for a different temperature. How does the measurement depend on the bias
ΔV?
From your measurement deduce the excitation energy and its uncertainty. Does your experiment
really measure the energy of the 3Po state in Hg, or is there a contribution from the other two 3P
states?
(C)
References:
[EDM83]
D.S. Edmonds, Cioffiari's Experiments in College Physics, Heath and Co., Lexington,
1983, p. 407.
[Wikipedia]
http://en.wikipedi.org/wiki/Franck-Hertz_experiment
Fig 3
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