PHYSICS 320 LAB

THE FRANCK-HERTZ EXPERIMENT

OBJECT:

To demonstrate, through the study of collisions between electrons and gas molecules, that the energy is indeed quantized in atomic interactions.

APPARATUS:

A mercury-filled Franck-Hertz tube, an electric oven, a control unit providing various power supplies and a DC current amplifier, and digital oscilloscope.

BACKGROUND:

Simplified Circuit for Franck-Hertz Experiment

In an oven-heated vacuum tube containing mercury gas, electrons are emitted by a heated cathode, and then accelerated toward a grid that is at a potential, V_a, relative to the cathode. The anode (plate) is at a lower potential, V_p = V_a - DV. If electrons have sufficient energy when they reach the grid, some will pass through and reach the anode. They will be measured as current I_c by the ammeter. If the electrons do not have sufficient energy when they reach the grid, they will be slowed by DV, and will fall back to the grid.  As long as the electron/molecule collisions are elastic, the collector current depends only on V_a and DV since the electrons lose no energy. However, Franck and Hertz discovered that I_c went through a series of maxima and minima as V_a was varied. This implies that the gas molecules absorb energy from the electrons only at specific electron energies (resonant energies).

For example, the first excited state of mercury is 4.9 eV above the ground state. This is thus the minimum energy that mercury atoms can absorb from the accelerated electrons. Hence, if V_a< 4.9 volts, any collisions are elastic and if V_a >DV, many electrons pass through the grid and reach the anode, to be measured as I_c. If V_a= 4.9 volts, the electrons gain enough kinetic energy to collide inelastically with the mercury atoms just when they reach the grid. In these interactions, the mercury atoms absorb 4.9 eV. Thus, the electrons lose the same amount and no longer have sufficient energy to overcome DV. They fall back to the grid and I_c is a minimum. As V_a is raised beyond 4.9 volts, I_c increases again. However, when V_a reaches 9.8 volts, the electrons can lose all their energy in two collisions with mercury atoms in two inelastic collisions between the cathode and grid. Again, these are pushed back onto the grid, and I_c falls to a minimum. Current minimum are found whenever V_a is a multiple of 4.9 volts.

This simplified description neglects contact potentials. Therefore, V_a will need to be some higher than 4.9 volts when the first minimum occurs. Nevertheless, all successive current minima should differ by multiples of 4.9 volts from the first minimum.

THE EXPERIMENT

• Insert a thermometer (0-200 °C) into the top hole of the oven and position the tip to be near the center of the tube. Plug the oven into an appropriate AC power outlet, then turn the thermostat dial to 180 °C. Keep an eye on the thermometer. Do not let the temperature exceed 205 °C.
• Connect the tube, control unit, and oscilloscope as follows. Note the German labeling:

  M = Plate or Anode

  A = Grid (not Anode!)

  H = Filament Heater

  K = Cathode

  Ub = Accelerating voltage Va



• AFTER the tube has warmed up 10 -15 minutes, switch on the control unit. Set the controls as follows:

Heater = midrange (about 5.5 volts)
Gain-Amplifier = midrange
Zero-Amplifier = midrange
Adjust V_a = zero
Switch V_a = ramp (a sawtooth waveform voltage)
Oscilloscope Channel 1 = about 0.5 volts/cm
Oscilloscope Channel 2 = about 0.5 volts/cm

• After the cathode has warmed up for at least 90 seconds, slowly increase the sawtooth voltage amplitude with the control knob U_b. The Franck-Hertz curve should appear on the oscilloscope screen. If necessary, improve the the display by judiciously adjusting the "gain" control and the cathode temperature "filament heating". Adjust the accelerating voltage such that no self-sustained discharge takes place in the tube. Otherwise, the curve is destroyed by collisional ionization.

ANALYSIS:

Note that on the oscilloscope trace the vertical deflection is proportional to the anode current I_c, and the input to the x-channel of the oscilloscope is equal to V_a/10.

Use the digital oscilloscope to average traces for both channels.  observe the traces in both the dual trace and X-Y modes.  Transfer these traces to a computer.  While you can observe on the oscilloscope the traces in X-Y mode, you will have to transfer the traces separately.  

Read the data into MathCad and plot the anode signal vs. the ramp signal.  From the plot, measure values of V_a for which the collector current (I_c) is a minimum. Then tabulate the voltage difference between adjacent minima.

You should find that the current minima are spaced at intervals of ~4.9 volts, showing that the excitation energy of the mercury atom is ~4.9 eV.

The spectral frequency corresponding to this energy is 1.18 x 10^-15 Hz and the wavelength is 253.7 nm.

In their original experiments, Franck and Hertz verified the presence of the ultraviolet radiation with the aid of a quartz spectrometer.