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 neon-filled Franck-Hertz tube, 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, Va, relative to the cathode. The anode (plate) is at a lower potential, Vp = Va - 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 Ic 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 Va and DV since the electrons lose no energy. However, Franck and Hertz discovered that Ic went through a series of maxima and minima as Va 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 Va< 4.9 volts, any collisions are elastic and if Va >
DV, many electrons pass through the grid and reach the anode, to be measured as Ic. If Va= 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 Ic is a minimum. As Va is raised beyond 4.9 volts, Ic increases again. However, when Va 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 Ic falls to a minimum. Current minimum are found whenever Va is a multiple of 4.9 volts.

This simplified description neglects contact potentials. Therefore, Va will need to be somewhat 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 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.

Neon has 10 energy states in the range between 18.3eV and 19.5eV.  From these excited levels, the Ne atoms decay to other excited states. These intermediate states decay to the ground state by emitting visible radiation and can be seen in a tube with the room darkened.

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. Since the thermostat on the Mercury F-H unit does not work, the temperature is controlled by a Variac variable AC voltage source. Switch the Variac to the 120V setting and monitor the temperature on the thermometer. The temperature should stabilize near 175 °C. Please 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 = a little less than midrange
Accelerating voltage = fully counterclockwise (Va)
Amplitude = nearly all the way counterclockwise
Reverse bias = fully counterclockwise
Switch Va = ramp (a sawtooth waveform voltage-60 Hz)

• After the cathode has warmed up for at least 90 seconds, slowly increase the accelerating voltage amplitude with the control knob. 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.  The accelerating voltage maximum should be about 30V.
• The neon tube doesn't require an external heater but it does have two more connections to be made with the Control unit.  The color coding and labeling should be followed.  The response is very sensitive to the heater setting - approximately 7.5 seems to work well.  If you're not getting nice symmetric peaks, try increasing/decreasing the temperature 0.5 - 1V.  Neon has 10 energy states in the range between 18.3eV and 19.5eV.  From these excited levels, the Ne atoms decay to other excited states and these states decay to the ground state by emitting visible radiation.
• ANALYSIS:

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

Use the digital oscilloscope to average traces for both channels.  Observe the traces in both the dual trace (time) and X-Y modes.  Explain why the current peaks are not evenly spaced in the dual trace mode.  Now transfer the two time traces to a computer.  While you can observe and take a screenshot of the oscilloscope in X-Y mode, you will have to transfer the traces separately and then recombine them in other software (preferably Origin) to analyze Ic vs. Va.

Import the data into Origin and plot the anode signal vs. the ramp voltage.  On the plot, use the cross-hairs tool to measure values of Va for which the collector current (Ic) is a minimum and compute the separation between adjacent dips.  Then tabulate the voltage difference between adjacent maxima.  Enter your DV measurements into a column in Origin, print the column for your records, and find the Descriptive Statistics on Columns option to compute a 95% confidence interval for your results. Clicking on the "Moments" plus button will let you select the quantities that you want to compute.

You should find that the current minima and maxima are spaced at intervals of ~4.9 volts, showing that the excitation energy of the mercury atom is ~ 4.9 eV.  Compare this energy with your 95% confidence interval and explain any deviation.

Repeat the analysis for the Neon tube.  You will need a higher Va and reverse bias for this tube.

Convert your excitation energy values for Hg and Ne in to nanometers and identify the EM spectral region in which they lie. Draw an energy level diagram for the two elements. How are the differences in them manifested in your Ic vs. Va data?

Think about the dips in current that your observe when the accelerating voltage reaches another transition threshold. How does the spread in kinetic energy of the incident electrons affect these dips? In other words, how would the dips be different if all of the electrons had exactly the same kinetic energy?