Download Franck-Hertz - University of Utah Physics

PHYS 3719 - Fall 2014
The Franck-Hertz Experiment
NOTE: Part of this material is taken from the PASCO manual; the apparatus used is structurally
identical to Pasco, but labeling is different. PASCO’s opaque nomenclature for the various
currents and voltages has been changed.
Introduction
The Franck-Hertz experiment allows you to demonstrate via electrical measurements that
electronic energy levels in atoms are quantized. You will also be able to measure the first
ionization energy of mercury as well as investigate the correlation between the mean free path
of electrons transiting mercury vapor and the current-voltage characteristics of the tube.
Experimental Setup
Required Equipment
SE-9640 Franck-Hertz Tube (Hg)
SE-9641 Franck-Hertz Oven
Power supplies to provide the following electrical needs:
- Filament Voltage, VF, 5 - 6.3 VDC (HP 6126A), supplies current to heat cathode
- Accelerating voltage, VGC, 0-30 VDC (Keithley 617, output to LabView)
- Opposing voltage, VAG, ≈1.5 VDC (D-cell)
Thermometer (to 200° C)
Ammeter with sensitivity to 10 pA (Keithley 617, programmed via LabView)
Shielded cable with a BNC and Triax connectors
DMMs to monitor voltages across filament, from the grid to the cathode and from anode to
grid.
A simplified diagram of the Franck-Hertz experiment is shown in Figure 1. In an oven-heated
vacuum tube containing mercury vapor, electrons are emitted by a heated cathode, and are
then accelerated toward a grid that is at a potential VGC relative to the cathode. Just beyond the
grid is an anode, which is at a slightly lower potential (i.e. negative with respect to the grid)
than that of the grid.
If the accelerated electrons have sufficient energy when they reach the grid, some of them
will pass through and will reach the anode. They will be measured as anode current IA, by the
ammeter. If the electrons don't have sufficient energy when they reach the grid, they will be
slowed by VAG, the potential difference between grid and anode, and will fall back onto the grid.
Whether the electrons have sufficient energy to reach the anode depends on three factors:
the accelerating potential VGC, the opposing potential VAG, and the nature of the collisions
between the electrons and the gas molecules in the tube.
NOTE: The above description is somewhat over-simplified. Due to contact potentials, the
total energy gain of the electrons is not quite equal to eVGC. Therefore, VGC, the potential
difference measured for the first current minimum, will be somewhat higher than the actual
first ionization energy of mercury. However, the contact potentials are a constant in the
experiment, so at successive current minima VGC will always be a multiple of the actual
ionization energy. Check this: is the energy of the first current minimum the same as the
difference between subsequent minima?
Figure 1. Simplified circuit diagram of the Franck-Hertz experiment.
About the Franck-Hertz Apparatus (Much of the following is from the PASCO manual)
The SE-9640 Franck-Hertz tube is a three-electrode tube with an indirectly heated, oxidecoated cathode, a grid and an anode. The distance between the grid and the cathode in the
Pasco apparatus is 8 mm, which is claimed to be large compared with the mean free path of the
electrons at normal experimental temperatures (180°C). This ensures a high collision
probability between the electrons and the mercury vapor molecules. The distance between the
grid and the anode is small to minimize electron/gas collisions beyond the grid.
- Estimate the cathode-grid and grid-anode distances in the Neva apparatus you are using and
comment on the previous statement based on your calculations of electron mean free path
length as a function of oven temperature (below).
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The tube contains a drop of highly purified mercury. A 10 kΩ current limiting resistor is
permanently incorporated between the connecting socket for the accelerating voltage and the
grid of the tube. This resistor protects the tube in case a main discharge strikes it when
excessively high voltage is applied. For normal measurements the voltage drop across this safe
resister may be ignored, because the working anode current of the tube is less than 5 μA.
- Calculate the voltage drop across the safety resister under typical conditions you use;
compare it to other voltages relevant to your experiment.
The tube is mounted to a plate which mounts, in turn, onto one wall of the SE-9641 FranckHertz oven (Figure 2).
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Anode
Grid
Oven thermometer
Heated cathode
Oven heater: vaporizes the mercury
Figure 2. Tube vacuum used in the experiment.
The SE-9641 Franck-Hertz Oven is a 400 watt, thermostatically controlled heater used to
vaporize the mercury in the Franck-Hertz tube*.
*
Unfortunately, the “thermostatic control” is relatively poor; hence we will set the thermostat to its maximum
value and supply the oven heater with a constant voltage from a Variac. The oven temperature – Variac voltage
correlation is posted on the wall behind the experimental setup.
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Caution: Even if you are familiar with the experiment, please read the section Important
Cautions and Tips [in the Appendix] before turning on the equipment. A few simple rules can
save you the cost of a blown experiment!
Instrumentation and Wiring
The Keithley 617 Electrometer has two functions: (1) it is programmed via Labview to supply
the accelerating voltage from the cathode to the grid (0-30V) and (2) it measures the current
into the anode. It outputs both of these values to the computer, which tabulates current as a
function of [ramping] voltage, the “answer”. It measures the current by means of a coaxial
cable with a BNC connector to the Franck-Hertz cell and Triax connector to the 617. The general
layout of all electronic components is shown in Figure 3. The voltage output from the Keithley
617 electrometer is via a pair of blue “Pomona” [brand name] patch cords with banana plugs,
as shown in Figure 4. A close-up of the Franck-Hertz faceplate, showing all connection points is
given in Figure 5. Note that the sheath of the BNC cable from the electrometer is internally tied
to ground, a fact not illuminated by the faceplate drawing (Figure 5). You may confirm this with
a DMM.
Figure 3. Complete setup of the Frank-Hertz experiment.
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Figure 4. Ponoma patch cord with banana plugs.
Figure 5. Close-up of the Franck-Hertz faceplate.
One of the Hewlett Packard 3466A DMMs measures this voltage. How is it connected?
A 1.5 V dry cell supplies the retarding voltage between the grid and the anode, and is
connected between the grid and the ground terminal, the objective of this voltage is to sharpen
the minima between peaks by removing from the anode current those electrons that have lost
energy in inelastic collisions and therefore have less than 1.5 eV of energy left. A second
Hewlett Packard 3466A DMM measures this voltage. For comparison, do at least one
measurement of I-V characteristics with this supply disconnected. Did it actually perform as
claimed?
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Experimental Procedure
Collecting Data
You will be measuring the current from the grid to the anode as a function of accelerating
voltage VGC, or the voltage from the cathode to the grid. The basic procedure for the FranckHertz experiment is straightforward:
1. Heat up the tube to approximately 170°C.
2. Apply the heater (Filament) voltage VF, to the cathode (wait 90 seconds for the cathode to
heat).
3. Apply an opposing voltage VA, (approximately 1.5 volts) between the grid and the anode.
4. Slowly raise the accelerating voltage (between the cathode and the grid, VGC) from 0 V to
about 30 V. Monitor the tube current to locate the potentials at which the current drops to
a minimum. You will not need to change VGC yourself; this process has been programmed
for you. Open “keithleyI-V”, which should be located on the desktop of the computer. This
program will plot the anode current against accelerating voltage, as well as produce a file
containing the data collected, which will be 2 columns of ASCII text (one of voltage and the
other of current). On the LabView screen, you will notice several parameters. Adjusting
them is fairly self-explanatory. The easiest way to organize your data is to first create a
folder. Open this folder, select the pathname for the folder and copy it into the text box
located under the “File Path” heading in LabView. Then under “data file” you may change
the name of the file to best describe the particular trial you are conducting, e.g. 5Vf,180C(2)
for the parameters VF = 5 V, T = 180°C, trial 2. Alternatively you can generate a table with
sequential numbers for file names and the values of appropriate operating parameters in
each column of the table. The data file can then be opened in e.g. Notepad or Excel, and
manipulated with data analysis software (e.g. Origin, Kaleidagraph, Excel, etc.).
The Hewlett Packard 6216A DC power supply supplies current to heat the filament, which is
directly attached to the cathode. The power supply output connects to points H and K on the
oven. Is the polarity of the connections important? Explain. If you set the voltage to a large
value, the current knob controls the current in the circuit; if you set the current to a large value,
the voltage knob controls the voltage applied to the filament. The Keithley 169 DMM monitors
the power supply output voltage; the current output of the HP 6216A current supply is
measured by the meter on the supply itself (when the switch on the front is correctly set).
Issues to be addressed
1) What is the contribution of the filament current to the experiment? What role does it play
in the testing of your model of what’s going on in the Franck-Hertz experiment? Is the exact
current critical? Run the experiment twice with voltages in the range 5.0 – 6.0 V or current
in the range 200 – 230 mA. Set the oven temperature to be in the range 150-200°C. Do your
data support your model of the role of the filament current?
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2) What is the contribution of oven temperature to the experiment? What role does it play in
testing your model of the Franck-Hertz experiment? Is the exact temperature critical? Run
the experiment several times with temperatures in the range 150-200°C. Use a filament
voltage within 5.0-6.0 V. What effect did you expect temperature to have on the
experiment? Do your data support the model of the role of the oven temperature?
3) With your understanding of the role of both factors in testing the model, i.e. the filament
voltage/current and oven temperature, run the experiment again selecting a value for the
filament voltage between 5.0 and 6.0 V or a filament current between 200-230 mA. The
temperature should be set within the range 150-200°C. What is the uncertainty in the
anode current that is measured by the electrometer, the “answer”? How will you decrease
your uncertainty? What methods can you use to determine the peak voltage? What is your
uncertainty in the peak voltage? What is your measurement, with uncertainty, of the lowest
excitation energy of mercury?
4) For each of the power supplies you are using, discuss whether the polarity with which you
connect them is important.
5) Except at the very lowest applied voltages, the current you measure with the electrometer
is always negative. Explain the significance of this sign.
6) If you invert the sign of the current, it is a lot clearer to describe the maxima and minima on
your plot. Explain what is going on at a maximum and at a minimum. (What physics causes
the I-V curve to exhibit a maximum or minimum?) Should you be measuring the differences
between maxima or minima?
7) What parameter contributes the maximum to the uncertainty on your results? What can be
done to improve your precision?
8) Using the value you obtained for the excitation energy, what wavelength would you expect
the emitted light to have? Can you see this light? Is it harmful?
9) Explain why your results support or refute the model being tested.
Appendix I (Optional for points extra credit)
Let’s do a sanity check on some numbers here by estimating the mean free path length of
electrons between collisions with mercury atoms and see how it compares to our apparatus
dimensions. From kinetic gas theory, the mean free path of gas molecules is given by
m = 1/(σn), where m is the mean free path length for molecules, σ is the collision cross-section
for interactions between molecules and n is the molecular density in the gas where molecules
are colliding. [You can find this expression in the kinetic gas theory section of any text on
Thermodynamics; in this case, from F. W. Sears, Thermodynamics, Addison Wesley, Reading MA
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(1953)]. Remember the ideal gas law: PV = nRT. But n in the expression for 𝜆𝑚 is really n/V, so
1/n is really RT/P. Here R is the Universal Gas Constant, which becomes Boltzmann’s Constant
since it refers to molecules rather than moles, T is the absolute temperature and P is the
pressure. The collision cross-section can be estimated as simply πr2, where r is the atomic
radius, given in the Sargent-Welch periodic table as 1.57 x10-10 m. The vapor pressure of
mercury as a function of temperature we can calculate from the generating function given by
Kubaschewski, Evans and Alcock, Metallurgical Thermochemistry, Pergammon (1967).
log10P(T) = A/T + B log10 (T) + CT + D where D = 10.355, A = -3305, B = -0.795 and C = 0; the
result, P(T), is in Torr. There could be an additional correction based on Paschen’s Law: buried
in the middle is the claim that since electrons are a lot smaller than molecules (and certainly
don’t interact like hard spheres) the mean free path length for electrons is greater than that for
molecules by a factor of “about 5.64”. Unfortunately this presents you with a major dilemma: a
search of the “conventional literature” leads one to observe that Paschen’s Law deals with
dielectric breakdown voltages in gases; no reference has yet been located supporting this
“magic” factor of “about 5.64”. So, it is now your responsibility to research the literature on the
mean free path of electrons in vapors like mercury, compare what you find to your data and
discuss the correlation or lack thereof. In any event, stuff all the information above into an
Excel sheet and calculate the mean free path length for electrons in mercury vapor at
temperatures of 25, 140, 150, 180 and 200°C and any others you may find useful.
Note that there are two temperature dependences in the mean free path: the linear one in
the density expression and the “exponential” one in the vapor pressure equation. Sanity check:
the Sargent-Welch table gives the boiling point of mercury as 357°C; does your generating
function give a reasonable confirmation of this? This example will give you lots of opportunities
to convert units, which physicists spend a lot of time doing.
Why are we doing this? Compare your calculated values of the mean free path length for
electrons at typical operating temperatures to apparatus dimensions given in the handout.
What happens at room temperature? Is there a big difference between 150°C and 180°C?
Appendix II
Important information from the PASCO Manual – Please read before using the Franck-Hertz
Apparatus:
Whether you are performing the experiment using the Control Unit or using separate power
supplies, the following guidelines will help protect your students and the equipment. They will
also help you get good results.
To Avoid Burns:
 The outside of the Franck-Hertz Oven gets very hot. Do not touch the oven when it is
operating, except by the handle.
To Protect the Oven:
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 Be sure the power to the oven is ac and is equal to the rated voltage for the oven. A dc power
supply or excessive ac power will produce arcing that will damage the bimetal contacts of the
thermostat.
To Protect the Tube:
 Always operate the tube between 150°C and 200°C – Never heat the tube beyond 205°C.
 Always use a thermometer to monitor the oven temperature. The thermostat dial gives the
temperature in °C, but the reading is only approximate.
 Turn the oven and allow the tube to warm up for 10-15 minutes (to approximately 170°C)
BEFORE applying any voltages to the tube.
Explanation: When the tube cools after each use, mercury can settle between the electrodes,
producing a short circuit. The mercury should be vaporized by heating before voltages are
applied.
 When possible, do not leave the tube in a hot oven for hours on end, as the vacuum seal of
the tube can be damaged by outgassing metal and glass parts.
 If the tube is left in a hot oven for a lengthy period of time, heat the cathode for
approximately two minutes and then apply an accelerating potential of approximately 5 volts
to the grid before turning off the oven. This will prolong the life of the cathode.
To Ensure Accurate Results:
 Use a shielded cable to connect the anode of the tube to the amplifier input of the Control
Unit.
 After heating up the tube in the oven, apply the heater voltage to the cathode, and allow the
cathode to warm up for at least 90 seconds before applying the accelerating voltage and
making measurements.
 Minimizing Ionization
Ionization of the mercury gas within the tube can obscure the results of the experiment
and, if severe, can even damage the tube. To minimize ionization, the tube temperature
should be between 150°C and 200°C and the accelerating voltage potential (between the
cathode and the grid) should be no more than 30 V.
Even if ionization is not severe enough to damage the tube, the positive mercury ions will
create a space charge that will affect the acceleration of the electrons between the cathode
and the grid. This can mask the resonance absorption that you are trying to investigate.
Ionization is evidenced by a bluish-green glow between the cathode and the grid. In fact, if
ionization occurs, the side of the grid facing the cathode will have a blue-green coating and
the cathode will have a bright blue spot on its center. If this happens, lower the accelerating
potential and check the tube temperature before proceeding.
Causes and dangers of ionization: If the tube temperature is too low, the mercury vapor
pressure will be low, and the mean free path of the electrons in the tube will be excessive. In
this case, the accelerated electrons may accumulate more than 4.9 eV of kinetic energy
before colliding with mercury atoms. This can lead to ionization of the mercury gas which can
increase the pressure inside the tube and damage the vacuum seal.
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If the tube temperature if too high, ionization can occur due to interactions between the
Mercury ions themselves. Again, pressure will be excessive and the tube can be damaged.
If the accelerating voltage is too high, the electrons can still gain excessive energy before
striking mercury atoms, even if the temperature is correct and the same problem can occur.
Reading Material
[1] PASCO manual (available in the teaching lab: South Physics building, Rm. 306).
[2] A.C. Melissinos and J. Napolitano, Experiments in Modern Physics, Academic Press, MA
(2003), Section 1.3.
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