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FRANCK-HERTZ EXPERIMENT
KEN CHENEY
5/22/2006
PICTURES
http://www.paccd.cc.ca.us/instadmn/physcidv/physics/teachers/cheney/lab%
20manuals/WEB%20Image%20Folders/Frank-Hertz%20WEB.pdf
ABSTRACT
The energy to excite mercury atoms will be measured to demonstrate the
existence of electron energy levels in atoms and to measure the energy
required to excite a ground state electron to the first excited state. The
effects of temperature, accelerating voltage, and mean free path will also be
investigated.
WARNING
The oven gets HOT; it doesn’t look hot so check before getting close!
HISTORY
Bohr (1913) showed that spectral lines could be explained by electron
energy levels in an atom.
Franck and Hertz (1914) showed that these same energy levels could be
detected with particles (electrons). This demonstration considerably
increased confidence in the existence of these energy levels, and earned
them a Nobel Prize in 1925!theory
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EQUIPMENT OUTLINE
A glass tube is heated to around 200C to vaporize mercury.
An anode (much as in a CRT) emits electrons that are accelerated toward a
grid by a voltage that sweeps from zero to a few tens of volts. Most of the
electrons will go through the grid.
On the far side of the grid from the anode is the cathode. The cathode has a
negative voltage relative to the grid so low energy electrons cannot reach the
cathode.
An oscilloscope is connected to plot the anode-grid (accelerating) voltage on
the x-axis and the current reaching the cathode on the y-axis.
Frank-Hertz Tube Schematic
Oscilloscope
y axis
A
Anode
Retarding
Voltage
Accelerating
Voltage
_
Grid
+
+
Oscilloscope
x axis
Hg Gas
_
Cathode
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THEORY OUTLINE
The “Accelerating Voltage” (Cathode to Grid) is greater than the “Retarding
Voltage” (Grid to Anode) so if nothing interferes all the electrons from the
cathode arrive at the anode and produce a current there.
If the electrons moving from the cathode to the grid collide with a mercury
atom the collision must be elastic if the kinetic energy of the electron is less
than the minimum energy (4.67eV) to excite the mercury atom. Since the
electron is much lighter than the mercury atom there is practically no energy
exchange.
However if the electrons moving from the cathode to the grid have enough
energy to excite an electron in the mercury gas the electron can lose 4.67 eV
if it excites the lowest energy state. More energy can be lost if it is
available, mercury has many energy levels above the lowest energy level.
The mean free path for collisions is much shorter than the distance between
the cathode and grid. Therefore if the electrons gain enough energy to excite
the mercury this will be very likely to occur. At low accelerating voltages
the electron may not gain enough energy while approaching the gird to
overcome the retarding voltage after passing the grid. These electrons will
never reach the anode; they will end up on the grid.
As the accelerating voltage is increased from a low value more and more
electrons can reach the anode so the anode current increases steadily. But
when the excitation voltage is reached suddenly most electrons lose energy
to excitations and then never get enough energy to reach the anode. The
anode current decrease very rapidly to a low value.
As the accelerating voltage continues to increase eventually the electrons
that have lost energy can gain enough energy to successfully excite the
mercury again, and the anode current decreases again. This process occurs
over and over again giving a succession of minimums in the anode current
separated by a voltage equivalent to the excitation energy plus a little more.
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WARNING
The oven gets HOT; it doesn’t look hot so check before getting close!
CONNECTIONS:
Klinger:
KA 6041 Franck-Hertz Oven
KA 6045 Franck-Hertz Operating Unit
Control
Unit
M FH
Signal
A
H
K Cathode
FH Signal
y-out
0…12v
Ground
Symbol
UB/10 xout
0…7V
PE Ground
Symbol
Oven Oscilloscope Digital
Voltmeters
M
Use
A
H
K
Grid
Filament Heater
Cathode
Voltage Proportional to
Anode current
Anode Current
Y input
Volts
Ground
Ground
Ground
X input
Volts
Cathode-Grid
Voltage/10
Not used
PRELIMINARY ADJUSTMENTS
WARNING
The oven gets HOT; it doesn’t look hot so check before getting close!
From the Klinger instructions:
1. Set the oven to the desired temperature. It takes a long time to
stabilize (hours?) so get this going at once.
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2. Before turning on the control unit turn the controls for “Heater”,
“Acceleration”, and “Amplitude” all the way down. Set “Reverse
Bias” to the center position.
3. Set the toggle switch “Man, Ramp/60 Hz” to “Ramp”. This will
sweep the accelerating voltage.
4. Oscilloscope
a. Connect the x to the "UB/10" (this is the accelerating voltage
divided by 10) and the y to the "FH Signal y-out"
b. Set the oscilloscope to xy mode so the x signal moves the trace
horizontally and the y signal moves the trace vertically
c. Adjust the x and y sensitivity for as large a pattern as possible,
you will have to change this from time to time.
5. Adjust the heater voltage to approximately 8v. This “heater” is the
filament to heat the cathode so it will emit electrons.
6. Adjust the accelerating voltage to 40v-50v.
7. “Amplitude” just changes the output voltage of the FH signal, it does
not affect the experiment.
8. The “Reveries Bias” is the retarding voltage. Adjust for the best
curve (lots of max and min).
9. Adjust the accelerating voltage to about 80v and tune the other
settings for the best curve.
ACCURATE READINGS OF THE VOLTAGES OF THE
MINIMUM ANODE CURRENT
Of course you cannot expect to read an oscilloscope very accurately. Do
expand the area of interest as much as possible, check that the knobs are on
“calibrate”, remember to multiply the x voltage by 10, use the curser if you
have on your oscilloscope, etc.
Much more accurate readings can be made with a pair of digital voltmeters.
1. Get a good curve and make a sketch showing your oscilloscope
readings for the accelerating voltages of the minimum.
2. Disconnect the oscilloscope and replace it with two digital
voltmeters.
3. Find the successive minimum of the FH signal (anode current), at
each minimum; record the UB/10 (accelerating voltage) on the
other digital voltmeter.
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TO DO
Check whether the energy differences (minimum to minimum) are close to
the minimum energy to excite mercury (4.67 eV).
MORE EXTENSIVE ANALYSIS
An article by Rapior, Sengstock and Baev in the American Journal of
Physics suggests a way to obtain much more information from this
experiment.
They suggest that after reaching the energy to excite a mercury atom ( Ea )
the electrons accelerate through one free path lambda (  ) before striking and
exciting a mercury atom and losing all their kinetic energy.
The mean free path is for reasonable conditions much shorter than the
distance between the cathode and grid (L) so the extra energy  n gained per
collision by this means is, for a voltage resulting in n collisions:
n  n

L
Ea
The total gained for n collisions ( En ) then is:
En  n( Ea   n )
(1)
The energy difference from one minimum to the next on the plot (remember
these are for different accelerating voltages):
 

E (n )  En  En 1  1  (2n  1)  Ea
 L

Notice that this difference is not Ea (as we might hope!) or quite linear.
(2)
We have measured E (n ) and n and we can (being careful not to get burned)
measure L. If we multiply (2) out (a form like y=A+Bn) we can do a least
squares curve fit to our data and extract Ea and  .
If there is time data obtained from other temperatures would give more
values to average.
 is a function of the tempter. The higher the temperature the greater the
vapor pressure of the mercury, hence the shorter the distance between the
mercury atoms. Equations quoted are:
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
1
kT
 B
N
p
(3)
and:
p  8.7  10(9(3110 / T )) Pa
(4)
Check as much of this is you can!
Symbols
T
p
Temperature in K
Pressure in Pascal
Mean Free Path

N
Atomic Number Density
Cross-section for collision with excitation, about (2.1  0.1)  1019 m2

Boltzman’s constant
kB
Lowest energy to excite mercury atom
Ea
Extra energy per collision for an accelerating voltage resulting in n
n
minimum (collisions)
L
Distance from cathode to grid
Energy gained by electron for the n’th minimum
En
E (n ) The difference in energy between minimum for n and n-1 collisions
n
The number of collisions resulting in exciting the atom
REFERENCES
Gerald Rapior, Klaus Sengstock, and Valery Baev, “American Journal of
Physics”, 74 (5), May 2006
FRANCK-HERTZ EXPERIMENT, Klinger Educational Products Corp.
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