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Critical Potentials
Edited 3/23/15 by Stephen Albright, DGH, JS
Part I: The Franck-Hertz Experiment
BACKGROUND: In 1914 German physicists James Franck and Gustav Ludwig
Hertz performed an experiment that supported the Bohr model of the atom and helped
pave the way for quantum mechanics. In their experiment they probed the energy levels
of the mercury atom. For their success with this now famous Franck-Hertz experiment,
they were awarded the 1925 Nobel Prize in Physics.
PURPOSE: Gain a better understanding of critical potentials and atomic energy gaps by
performing a close approximation of the original Franck-Hertz experiment.
To become more familiar and proficient with experimental techniques and procedures.
APPARATUS: Franck-Hertz tube w/ oven, electrometer, three DC voltage sources,
function generator, oscilloscope.
REFERENCES: “Modern Physics”, by Tipler & Llewellyn, pp. 185-188; “Modern
Physics from α to Z0”, by Rohlf, pp. 82-83.
WIKI REFERENCES: See the PHYWE “Franck-Hertz Manual” and “Franck-Hertz
Oven” under “Equipment Manuals & References” on the Lab Wiki. The other FranckHertz related documents on the lab wiki may also be helpful
FRANCK-HERTZ TUBE: The Franck-Hertz tube is a triode with three plane, parallel
electrodes: an indirectly heated oxide-coated cathode, a grid (fine screen) and an anode.
The distance between the cathode and the grid is large compared with distance between
the grid and the anode. More importantly, the distance between the cathode and the grid
is large compared with the mean free path of the electrons in the Hg vapor whereas the
distance between the grid and the anode is short by the same comparison. Therefore, the
impact probability is high between the cathode and the grid but quite low between the
grid and the anode. Electrons in the Franck-Hertz tube will be accelerated across a
potential difference; these accelerated electrons will collide with the mercury vapor in the
tube and force atomic transitions. These transitions are observed as periodic variations in
the tube’s anode current.
OVEN: The oven is used to warm the tube to somewhere between 120-200°C. This will
vaporize Hg in the tube. Note: the Hg in the tube is not ionized by this process. Though
the ovens are designed to be plugged directly into a 110V AC wall outlet, we will be
plugging them into a Variac, this will give us better temperature control. The large knob
on the side of the oven should always be set fully on (10). The temperature of the oven
will be monitored via a digital thermometer inserted through a hole in the top of the oven.
The tip of the thermometer should be located near the tube filament (the red glow).
NOTES:
• Due to variations in oven temperature, slightly different levels of collection
current may be obtained for measurements repeated at the same acceleration
voltage. However, the position of the maxima will be unaffected.
• The position of the collection current maxima is not affected by changes in the
reverse bias (retarding potential). However, changes in the reverse bias will
displaced the position of the current minima a little.
• The level of the mean collection current decreases with increasing reverse bias.
Figure 1: Schematic of the manual Franck-Hertz experiment
WARNING:
1. When the oven is on, its housing, screws, connectors and handle will be very hot!
2. Do not apply a voltage to the filament before pre-heating the oven, this could
cause a short circuit between the tube’s electrodes through the liquid mercury.
PROCEDURE - MANUAL MEASUREMENT:
Start by plugging in the oven to the Variac and the Variac to the wall. Set the Variac to
3A so that the oven is heated to ~150C by the time you are ready to take data. Be
careful, the oven will get hot as you are connecting wires to it, so don’t touch it directly.
Connect your equipment as shown in Figure 1. Note: The oscilloscope and function
generator will not be used in this setup. Pay particular attention to the ground
connections: remember that ground connectors are connected to each other through the
ground. It is easy to inadvertently create a short circuit through ground connections. Do
not turn any power supplies on until the TA has confirmed that your wiring is correct.
DO NOT plug in the 6.3V power supply until the cabinet temp is greater than 120 o C.
Set the 60V power supply to 0V and the electrometer to “Zero Check”. Set the retarding
potential to 1.5V. Turn on the 60V supply and set the Variac to ~3A. Do not plug in the
6.3V supply. In a little while the temperature should stabilize at about 150°C. Once the
temperature is above 120 o C, you may plug in the 6.3V power supply. Set the
electrometer to 00.00 nA and turn off “Zero Check” – do not use the “autoscaling”
function. Once the temperature has stabilized the apparatus is ready to take data as
follows:
1. Use the fine voltage control knob on the 60V power supply to slowly increase the
accelerating potential. Starting @ 4V, record the current and voltage in 0.2V
intervals. At least one current minimum should be observed before 12V.
2. Making use of both the coarse and fine adjustment knobs, scan larger voltages for
other troughs. Take measurements around the current minimums as you go
higher.
3. It will likely be necessary to change scales on the electrometer but do not use the
“autoscaling” function.
4. At some point there will be a huge spike in anode current and a blue glow will be
visible in the tube. This is called the “critical potential”, it occurs when the Hg
vapor is ionized. To recover from this condition, reduced the accelerating
potential until the anode current returns to normal. Take note that the ionization
exhibits a hysteresis effect: going down it remains ionized at potentials much
lower than it originally ionized going up. Be careful not leave the tube at the
ionization potential for long, the tube may be damaged. To collect data at higher
accelerating potentials, the oven temperature must be increased. See The Wiki
References for more information.
QUESTIONS:
1. Why is the first current maximum found at an acceleration voltage above 4.9V?
(hint: Do the electrons start free? Also, what effect does the retarding potential
have on the energy of the electron? You may want to try sketching a plot of the
potential the electron sees as it travels from the cathode to the anode.)
2. Why is the separation between all of the peaks constant?
3. What are the wavelength and energy of the spectral line emitted by this transition?
PROCEDURE - AUTOMATIC MEASUREMENT:
To automate the data collection process, the function generator and oscilloscope will be
added to the circuit. Before assembling the new circuit, turn the 60V power supply off,
set the electrometer on Zero Check, and lower the Variac to ~2.7A. The temperature
should eventually stabilize at about 130-140°C.
While the heater is cooling, assemble the circuit displayed in Figure 2. This should not
require major rewiring. Notice the effect of connecting the function generator in series
with the 60V DC power supply. Now, instead of applying a constant acceleration
potential to the grid, a varying acceleration potential can be applied – the varying voltage
of the function generator is riding on top of the DC offset voltage of the power supply.
This allows measurement of a wide range of potentials in rapid succession. Warning:
Do not casually connect power supplies or other output devices in series. It is important
to know where ground is and how the device responds to riding on a DC offset potential,
failure to take these matters into consideration could cause the destruction of one or both
of the devices.
Figure 2: Schematic of the automated Franck-Hertz experiment
1. Initial Setup:
a. Turn on the oscilloscope. Press Menu > Recall Setup > Setup1 > Menu
Off. This will initialize the scope.
b. Set the time scale to 2 sec/div, Ch 1 to 20 mV/div and Ch 2 to 5 V/div.
Set both channels to invert. Press FilterVu, turn off “glitch capture” and
set the frequency to 29 Hz. Scroll both channels to the bottom of the
screen; this will make the waveforms visible during taking data.
c. Set the 60V power supply to 0V and turn it on. Set the power supply to
10V.
d. Turn on the function generator and, set it to a 0.05 Hz sawtooth wave at
10V P-P as read on the High Z setting.
e. Set the electrometer to 00.00 nA.
2. First measurement in 130 – 140C.
a. When the heater has stabilized (between 130 and 140°C), release Zero
Check on the electrometer. There should be a scanning waveform on both
channels of the scope. Ch 2 displays the voltage applied to the grid, Ch 1
the current measurement from the electrometer.
b. Adjust the voltage scale of Ch 1 to get clear peaks – they should
correspond to the first two peaks measured in the manual-measurement
experiment.
c. When a satisfactory waveform is displayed, press Run/Stop and save the
data to the supplied flash drive. After saving, press Run/Stop again to
allow the waveform to scan.
d. You will want to make sure that you are getting quality data for both
channels readable my Excel / Kaleidagraph. This is important so that you
can plot the current directly as a function of voltage instead of time.
e. Take note of the voltage at which the mercury ionizes.
3. Now, set the Variac to 3.0A and repeat the automated measurement of the current
profile once the temperature stabilizes around 150C.
a. At this temperature, you should now have enough leeway to get at least 3
peaks on the screen beneath the ionization potential.
b. You will need to increase the accelerating potential offset (on the DC
power supply) and pk-pk voltages (on the wavefunction generator) in
order to probe these voltages in one sweep. Be careful not to exceed 40V
total (which would be = DC voltage + ½ Pk-Pk Voltage).
c. You may also need to change the scales substantially on the oscilloscope
so that the signal takes up the whole screen, which is necessary to
maximize the precision of the signal.
d. Again take note of the ionization potential.
4. Do the same at around 180C by setting the Variac to 3.5A and waiting for the
temperature to equilibriate.
a. You should be able to get a nice image of 4 peaks at this temperature.
b. You may not be able to observe the ionization of the gas under 40V. This
is fine, just note that the gas ionizes at >40V.
5. Investigate the impact of the retarding potential by taking another 4-peak data set
using 3V (both D-cells) in series and comparing the data in your analysis.
6. Once measurements are completed, set the electrometer on Zero Check, turn
down the 60V power supply, turn off all of the power supplies and turn the Variac
down to 0A. WARNING: Be sure to unplug the 6.3V supply to the filament
immediately (while hot). Do not disassemble the circuit, as many of the
connections will still be hot from the oven.
QUESTIONS:
1. What effect does the temperature of the tube have on the measured current? What
happens to the current peaks at low accelerating potentials with increasing
temperature? Explain both of these effects.
2. Why does a higher oven temperature produce a higher ionization potential? (Note:
this is a particularly challenging question and you are not expected to come up
with the correct answer necessarily. Just be sure to propose something that
makes sense under moderate scrutiny and back it up with a few sentences of
reasoning. If you’d like, you can consult (and cite) outside sources to make your
argument.)
3. Explain the effects of retarding potential on the relative size and position of the
current peaks.
Part II: Critical Potentials of Neon
BACKGROUND: In the Franck-Hertz experiment, the same energy gap of Hg is
measure repeatedly. It turns out the design of the experiment prohibits the measurement
of other energy gaps. In this experiment, in addition to using neon gas, there have been
some subtle but significant changes to the tube configuration and how it is wired that will
allow the collection of a series of energy gaps.
PURPOSE: Gain a better understanding of critical potentials and atomic energy gaps by
performing a variation of the Franck-Hertz experiment with neon gas; explore the
differences in configuration and technique that allow the measurement of multiple atomic
energy gaps rather than one gap as in the Franck-Hertz experiment.
APPARATUS: Neon tube, 0-8V DC power supply, 0-60V DC power supply, function
generator, oscilloscope, electrometer and a 1.5V battery
WIKI REFERENCES: See the Telatomic “Neon Critical Potential Tube” on the Lab
Wiki. The other critical potential related documents on the lab wiki may also be helpful
CRITICAL POTENTIAL TUBE: The Critical Potential Tube shown in Figure 3 contains
a “cathode ray gun” which projects a divergent beam of electrons into a clear glass bulb.
The bulb contains low pressure neon gas. Inside the bulb is a wire ring collector
positioned such that it cannot receive electrons directly from the cathode. The ring is
connected to a shielded cable. The cylindrical anode of the “gun” is connected to the
inside surface of the glass bulb, this surface is coated with a transparent conductor. The
wire ring is insulated from this conductor.
Figure 3: Schematic of the manual Neon Critical Potential Experiment
PROCEDURE - MANUAL MEASUREMENT: As in the Franck-Hertz experiment,
manual current measurements will be taken first followed by automated measurements.
Note: In this experiment, current peaks identify the critical potentials. Why is this?
Take data as follows:
1. Setup Figure 3. Be gentle with the neon tube and holder, they are fragile (and
temperamental). Pay close attention to the inputs of the tube holder (F4, F3 and
A1). The inputs are located on the back of the holder while the labels appear on
the front, beneath the tube. Remember to pay particular attention to ground
connections as instructed in the Franck-Hertz experiment. Do not turn any power
supplies on until the TA has confirmed that your wiring is correct. Note: The
oscilloscope and function generator will not be used in this configuration.
2. Have a TA check your wiring before continuing.
3. The electrometer should be on, turn on Zero Check and set the range to 0.000 pA.
4. Set the 0-3V (retarding) potential to 1.5V. Set the accelerating power supply to
0V and turn it on. Turn on the filament power supply. Note: The filament supply
is set, do not adjust it. If the filament supply displays zero current, contact the TA.
5. Turn the course knob of the accelerating power supply to ~10V and release Zero
Check.
6. Begin increasing the accelerating power supply in 0.2V steps and record the
current at each step.
7. You should see two peaks in current before 17V. Decrease the voltage step size
to 0.1V while in and near the peaks.
8. Scan (without taking regular measurements) higher voltages until you observe
another set of peaks. Again record data in 0.1 V steps while in and near the
second set of peaks. The second set of peaks should occur before 35V.
9. Once measurements are completed, set the electrometer to Zero Check, turn down
the 60V power supply and turn off all of the power supplies.
Figure 4: Schematic of the automated Neon Critical Potential Experiment
PROCEDURE - AUTOMATIC MEASUREMENT:
As in the Franck-Hertz experiment, data collection will now be automated by adding the
function generator and oscilloscope to the circuit. Before assembling the new circuit,
turn the 60V power supply off and set the electrometer to Zero Check. Assemble the
circuit displayed in Figure 4. This should not require major rewiring. As before, this
configuration will allow data to be collected and displayed on the scope.
1. Turn on the scope and press Menu > Recall Setup > Setup1 > Menu Off to
initialize the scope.
2. Set both channels to invert. Set Ch1 to 50mV and Ch2 to 5V. Set the Horizontal
Scale to 4 sec/div. Scroll the Vertical position of both channels to the bottom of
the screen. Press “FilterVu”, set “Glitch Capture” off and “Noise Filter” to 14 Hz.
3.
4.
5.
6.
Turn on the filament power supply, offset power supply and function generator.
Set the function generator to 0.05 Hz and 10V P-P on High Z.
Set the offset supply to 15V P-P.
Set the electrometer to 0.000 pA and release Zero Check. There should be a
scanning waveform on both channels of the scope. Peaks similar to those found in
the manual measurement should be present.
7. Adjust the pA setting of the electrometer and the voltage of Ch1 to get the largest
peaks possible without going off of the screen.
8. Adjust the offset voltage as necessary to optimize the location of the peaks.
9. Record the values of the power supplies, function generator and electrometer.
Save both scope channels to the flash drive.
10. Systematically increase the offset voltage until you find the second set of peaks at
higher voltages.
11. When you find the second set of peaks, optimize their appearance on the scope and
repeat step 9.
12. Change the retarding potential to 3V and repeat steps 4-11. What effect does the
retarding potential have on these critical potential peaks and why?
13. Identify the wavelength of the transition associated with each of the peaks you
recorded. Again, refer to the “references and resources” section of the wiki.
Figure 5: Absorption Spectrum of Neon