Franck-Hertz Supplementary Guide
CAUTION: Do not turn on the Franck-Hertz operating unit. DO TURN ON the
heater in the Franck-Hertz experiment unit. Set the temperature control knob low
on the right side to about 190. Look through the back of the oven unit to verify that
the thermometer bulb or temperature sensor is located at the same height as the
center of the tube. (If a thermometer is not available, the temperature in the
experiment unit is to be monitored using a thermocouple. Set the attached
multimeter to oC. The meter should begin displaying the temperature.) Wait at least
15 minutes before energizing the operating unit. Use the time to read this guide.
Even after 15 minutes, do not energize the operating unit unless the reported
temperature is greater than 150 oC.
Goal: Reduce you data and then address the question: Do your results suggest he
existence of discrete energy levels in Hg? If so, what value is suggested for an
excitation energy of Hg . Include any observations that you make about the
behavior of the apparatus. Compare your excitation energy suggestion with the
known level diagram for mercury.
SETUP: Verify that a banana plug wire is connecting the A jack on the operating
unit to the A (acceleration potential1) jack on the experiment/oven unit. Repeat for
the H(heater) and K (cathode) jacks. Verify that a coax cable connects the M jack
on the operating unit to the M jack on the experiment unit. There should not be any
other connecting wires between the two units. The connections to the oscilloscope
(or the data acquisition module) should both use the ground connection (14)
between and the connections 13(the accelerating potential  10) and15 (the
amplified picoammeter output.).
Set the (Heizung) Heater on setting 8 after the Operating Unit is energized.
The setting may be raised to values up to 12 during data runs. Adjust for best
1
There is some dispute about calling this connection the anode. Some would call it a control grid and call the plate
above the control grid the anode. For definiteness, we will call A the control grid. The anode is the connection at
which positive current enters a device. We have electrons exiting at M, being retarded and collected for
measurement.
F-H.1
Franck-Hertz Supplementary Guide
outcomes. When not taking data, return the Heater setting to 8. Once you
have your data turn down the accelerating voltage and then the heater. Turn
off the operating unit and then set the temperature control to its lowest
setting. Tube filaments are a primary failure point. (Heizung) Heater: Do not
operate filaments at high currents for extended periods. This caution should
be extended to the electron diffraction tube, the blackbody lamp, … . Do not
‘abuse’ the equipment. Report procedures that you adopt to minimize stress
or wear on your apparatus.
Apparatus Connections Figure: The components illustrated are the Operating
Unit, the Control Unit and the Data Display. While an oscilloscope is used as a
display here, we can also capture the data Using the Pasco interface and Data
Studio to allow us to collect and manipulate the data.
F-H.2
Franck-Hertz Supplementary Guide
Tube Schematic and Operating Unit Image: The tube is enclosed in the
operating unit which provides connections to the tube and which acts as a
temperature controlled oven that sets and regulates the vapor pressure of the
mercury in the tube.
The grid is perforated allowing a
fraction of the electrons to pass
through to the collection anode.
There is a small retarding potential
(about 1.5 V) which the electrons
must overcome to pass through the
picoammeter. The retarding voltage
favors electrons that pass cleanly
through the perforated grid. The
important point is that the electrons
only lose energy to the mercury
atoms if they have enough energy to
excite the mercury and the mercury
is dense enough that the electrons
will collide and lose energy before
they gain much more.
In neon, the lowest excitation
energy is higher, and visible light is
emitted as a result of the collisions.
One can visually track the regions in
which the electrons accelerate and
regions in which the fill gas is
excited in a neon F-H experiment.
Frank-Hertz in Neon Image
The light emitted in the case of
mercury is ultraviolet, and it is
absorbed by the envelope of the
tube. We will see nothing
http://www.youtube.com/watch
?v=zMPO1JEKHZE
http://www.youtube.com/watch
F-H.3
Franck-Hertz Supplementary Guide
?v=0Vx0tKmaZ1k
Control Unit connections for The Franck-Hertz experiment using mercury.
1 Franck-Hertz Current Collector signal
2 Collector signal amplification adjust
3 Retarding Potential
4 Power switch
5 Neon tube output DO NOT USE
6 Fixed V to Ramp toggle switch
7 Grid Accelerating Potential Out
8 Adjust Accelerating Potential
9 Heater Voltage Out
10 Adjust Heater Voltage keep < 7 V
11 Cathode Connection
12 Chassis Ground DO NOT USE
13 Monitor Accelerating Voltage  10
14 Signal/Measurement Ground
15 Monitor F-H Current Collector signal
F-H.4
Franck-Hertz Supplementary Guide
Introduction
The Franck-Hertz experiment verifies that the atomic electron energy states are
quantized by observing maxima and minima in transmission of electrons through
mercury vapor. The variation in electron current is caused by inelastic electron
scattering that excites the atomic electrons of mercury. As the electrons lose
energy, their speed and hence the current are reduced.
The 1925 Nobel Prize in Physics was awarded jointly to Franck and Hertz for their
discovery of the laws governing the impact of an electron on an atom. The
experiment provided additional evidence for the existence of discrete energy levels
in atoms and thus supported quantum mechanics2.
The theoretical background for this experiment can be found in:
Experiments in Modern Physics by Adrian Constantin
Melissinos and Jim Napolitano beginning on page 10. What
role does the temperature play? How would your current vs.
accelerating voltage plot change if the density of mercury were
too high or too low? Interpret your plots for various
2
The phrase "quantum mechanics" was first used in Max Born's 1924 paper "Zur Quantenmechanik".
F-H.5
Franck-Hertz Supplementary Guide
temperatures in the range 150 to 230 and voltages from 0 to 80.
Reduce the voltage as soon as the tube picoammeter pegs.
Theory: The Frank-Hertz tube contains mercury vapor, and the density of that
vapor is controlled by changing the temperature of the tube. A heater maintains the
tubes at a temperature warmer than its environment. Unfortunately, the heater has a
bang-bang controller. That is: The heater turns on at full power and remains on full
until the tube reaches a preset Tmax and then turns off. The heater remains off until
the tube reaches a present Tmin at which point it turns on at full power again. You
might monitor the temperature to ascertain the values of Tmax and Tmin for each of
your measurement runs so that you can estimate the range of vapor pressures. The
electrons gain (kinetic) energy as they travel toward the grid. Electron collisions
with the mercury atoms must conserve energy and momentum which ensures that
the electrons lose very little energy in collision with the atoms unless the mercury
atom is excited as a result of the collision.
Question: What is the mass ratio for mercury atoms and electrons? Consider a 1D
elastic collision in which a moving electron strikes a mercury atom at rest. What
fraction of the electron’s initial kinetic energy is transferred to the atom as a result
of the collision?
F-H.6
Franck-Hertz Supplementary Guide
Just for definiteness, we assume that the electron gains enough energy to excite a
mercury atom after being accelerated though a distance of 2 mm. We want the
mercury density to be high enough that the electron has many collisions in 2mm to
ensure that, after the electron has gained enough energy to excite an atom, it is has
several more collisions before its energy becomes very much larger than that
needed to excite an atom. We do not want to increase the density of Hg much
beyond the value needed because the net current decreases as the mercury density
increases. It is difficult to accurately measure 100 pA currents. Measuring 1 pA
sized current accurately is too difficult. When the electron excites an atom, it loses
most of it kinetic energy leading to a decrease in its contribution to the current.
That is, we expect a dip in the current through the tube each time the electron gains
another multiple of the mercury excitation energy.
Question: Would you expect the second dip or the seventh dip to be sharper (have
a narrower width in terms of the applied accelerating voltage? Discuss.
Question: What is the definition of voltage? en.wikipedia.org/wiki/Voltage
Measurements: The data desired is the current from M to A through the
picoammeter as a function of the accelerating potential between the grid and
cathode K at several different temperatures in the range 150 to 220 CO. Discuss
your results. What trends do you see in the dip locations as the temperature
increases? Compare the outcome to an energy level diagram for mercury. Interpret
your results and there importance to the acceptance of quantum mechanics. Note
that the operating unit provides a terminal output for the accelerating voltage
F-H.7
Franck-Hertz Supplementary Guide
 10. Measuring instruments have limited ranges. The  10 feature provides
voltage monitor that is proportional to the accelerating potential and which is less
than 10 volts, the highest input voltage for the PASCO interface. Check the
allowed range for the Pasco interface before using it.
Data Acquisition: You should be able to record and analyze your data in the
Data Studio environment.
Goal: Reduce you data and then address the question: Do you results suggest he
existence of discrete energy levels in Hg? If so, what y would you suggest for the
excitation energy of an excited state of Hg as relative to its ground state. Include
any observations that you make about the behavior of the apparatus. Compare you
energy level suggestions with the known level diagram for mercury.
Note that the oscilloscope image above represents ideal data. Your efforts will
probably yield less well-defined dips.
F-H.8
Franck-Hertz Supplementary Guide
Shown for a thermocouple temperature sensor. We use a thermometer.
F-H.9