\experiment{The Franck-Hertz Experiment}

This experiment was performed by Franck and Hertz in 1914, following
by one year Bohr's publication of the theory of the hydrogen spectrum.
The Bohr theory, using Rutherford's nuclear atom, is based upon a
mechanical model---an electron circling about a proton in a manner
described by a new law of mechanics. The observations supporting the
theory, and which necessitated a new description of atomic systems,
were electromagnetic. Light is emitted and absorbed by atoms. The Bohr
theory of hydrogen was a success because the energy difference between
the various mechanical states of the electron-proton system
corresponded, through the Einstein frequency condition $E =h\nu$, to
observed frequencies of emitted and absorbed radiation. The
Franck-Hertz experiment, on the other hand, was a direct mechanical
confirmation of an essentially mechanical theory.

The optical spectrum of mercury vapor shows distinct emission and
absorption lines corresponding to transitions between discrete energy
levels of the mercury atom.  Franck and Hertz found that discrete
transitions of the mercury atom could also be produced by the inelastic
scattering of electrons from the atom. Consider the system of an
electron with some initial kinetic energy incident upon a mercury atom
at rest in the ground state. If the electron energy is less than the
energy required to excite the atom to its first excited state, the
collision must be elastic. The kinetic energy of the electron-atom
system cannot change. Due to the disparity of masses, the kinetic
energy of the electron itself is essentially unchanged in the
collision. If the electron energy equals or exceeds the energy for
exciting the first level, however, the collision may in some cases be
inelastic. The kinetic energy of the system is, in these cases,
different after the collision than before.  In an inelastic collision
some of the initial kinetic energy is converted to potential or
``excitation'' energy of the atom. In due course, this energy is
radiated from the excited atoms as light, but the primary interaction
is one described in mechanical terms. Franck and Hertz observed such
inelastic collisions by monitoring the current of electrons passing
through a mercury vapor.

\section{Apparatus}

\begin{figure}[t!]
  \centering
  \ig[1]{FranckHertzApparatus}
  \label{fig:FranckHertzApparatus}
  \caption{Franck-Hertz Electron Tube and Circuit.}
\end{figure}

The apparatus consists of a special electron tube containing a small
quantity of mercury. The vapor pressure of mercury in the tube is
adjusted by placing the tube in a furnace whose temperature may be
varied. Electrons emitted from the cathode must, then, traverse a
controlled mercury atmosphere in reaching the anode of the tube (see
\fref{FranckHertzApparatus}).


The anode is perforated so that many of the electrons will pass
through it and collect on the counter-electrode. 

Emission current from the cathode is controlled by the temperature of
the cathode and by the potential applied to the anode. A diaphragm
connected to the cathode limits the current and eliminates secondary
and reflected electrons, making the electric field more uniform.

Electrons which pass through the hole in the diaphragm are accelerated
through the mercury atmosphere by the positive potential applied to
the anode. The counter-electrode is maintained at a potential of
approximately \val{-1.5}{V} with respect to the anode. Thus no
electrons which pass through the perforated anode with energy less
than \val{1.5}{eV} can reach the counter-electrode.

If the electrode and the cathode were of the same material and if all
electrons were released from the cathode with zero kinetic energy,
then the current of electrons collected by the counter-electrode would
vary with the anode potential in the following way. No current would
be observed until the potential of the anode exceeded \val{1.5}{V}. As
the potential is increased, all electrons passing through the anode would
reach the counter-electrode and the current would show a continuous
increase with rising potential until a potential corresponding to the
energy transition from the ground to the first excited state of
mercury is reached. At this point the current would drop abruptly with
increasing potential, since many electrons would make inelastic
collisions with mercury atoms and have insufficient kinetic energy to
reach the counter-electrode. If the potential were sufficiently
increased, however, the electrons would again reach the
counter-electrode even after making an inelastic collision. This
second increase in current would continue until the electrons gained
enough energy to make two inelastic collisions, again not being left
with enough kinetic energy to reach the counter-electrode. This would
result in a second sharp drop in current. If the above conditions were
satisfied, a succession of current maxima with sharp breaks would be
observed with increasing potential.

The fact that the counter-electrode and the cathode may not be of the
same material makes the first maximum an unreliable measure of the
excitation potential of mercury. A so-called ``contact'' potential
must be added to or subtracted from the observed potential. Evaluation
of the contact potential is avoided by measuring potential differences
between succeeding maxima. The fact that electrons are not emitted
from the cathode with zero kinetic energy means that the actual energy
distribution is superimposed upon that established by the anode
potential. Sharp breaks are thus washed out of the current-voltage
curve.


\subsection{Electrical Circuit}

The circuit employed in this experiment is shown in
\fref{FranckHertzApparatus} All voltage sources indicated in the
figure are located in a power supply which is connected to the furnace
by means of various power cables. The measuring amplifier is a
separate unit, but the microammeter which reads the counter-electrode
current is mounted in the front of the power supply. A voltmeter
(0--50~V) on the front of the power supply reads the anode potential,
and a third small voltmeter is used for the bias voltage and the
voltage across the filament. Filament current is supplied by a
\val{6.3}{V} transformer and bridge rectifier. The anode and bias
potentials are derived from dry cells mounted inside the power
supply. All potentials are controlled by knobs on the front of the
power supply. There are also two switches on the front of the power
supply, the ``\textsc{Power}'' switch and the ``\textsc{Anode}'' switch.  Filament
potential alone is supplied with only the \textsc{Power} switch on. The \textsc{Anode}
switch must be on for both anode and bias potentials.

\section{Procedure}

The oven in which the tube is mounted should be turned on immediately
upon entering the laboratory.  The temperature inside the oven is
controlled by an external regulator. A thermometer protruding from the
top of the cabinet provides a measurement of the temperature near the
mercury tube. Close attention should be given to the reading of the
thermometer so that a temperature of \degC{180} is at no time exceeded. By
means of the thermostat control knob, the temperature of the oven
should be adjusted initially to \degC{170} $\pm \degC{5}$. Check the
oven temperature every few minutes. 

The Leybold measuring amplifier should also be turned on immediately
so that it will have ample time to stabilize. As the temperature of
the tube approaches its operating value, the power supply
\textsc{Power} switch
should be turned on.

Set the sensitivity range of the measuring amplifier at $30 \times
10^{-10}$, turn the sensitivity control knob to its central position,
and zero the microammeter by means of the ``zero'' control knob on the
amplifier. The input signal to the amplifier may be grounded at the
time these settings are made, but the grounding connection on the
front of the amplifier must be turned off, $\theta$, before any
current measurements can be made.

When the operating temperature is reached, \scream{first make sure
that the \textsc{Anode} voltage control knob is turned to the full
counterclockwise (zero) position}; then turn the \textsc{Anode}
switch on.

Increase the filament voltage to the value suggested at your
station. Slowly increase the anode potential to about
\val{35}{V}. Watch the microammeter carefully. \scream{If the current
  increases suddenly, an electrical breakdown has occurred in the
  tube, and the potential must be reduced to zero immediately.} If
such a breakdown has occurred, reduce the filament voltage very
slightly and again try to raise the anode potential to
\val{35}{V}. (If the tube still breaks down, see your instructor.) Now
very slowly increase the anode potential to \val{40}{V} and adjust the
sensitivity knob to give a full scale deflection of the microammeter
for the maximum current observed in the 30--40~V range. Allow
time for the current to stabilize after each small adjustment and
watch out for the onset of electrical breakdown.

The apparatus is now ready for taking measurements. Slowly decrease
the anode potential and observe the microammeter deflection. Dips and
peaks in the current should be obvious in the 0--40~V range. The
sensitivity range of the amplifier may have to be changed in order to
define the maxima clearly at the lower anode voltages. Record
counter-electrode currents vs.\ anode potential. Note that small
temperature changes will affect the current at a given voltage (why?),
so monitor the oven temperature as you make your measurements. Plot
your data and determine the excitation energy of mercury. Repeat your
measurements while slowly increasing the anode voltage from 0 to
\val{40}{V}. Repeat with different oven temperatures. (Do not exceed
\degC{180}.)  For each temperature you should reset the sensitivity knob
following the original procedure. From all your data obtain your best
estimate of the excitation energy of mercury.
