3. Frank-Hertz type Experiment with Helium

3.1 Theory^*

Figure 4 shows a typical IV curve produced when an electron beam is accelerated through He gas by a voltage V_A to a collector ring, producing a current I_C:

Figure 4: Typical IV curve for He gas in a Frank-Hertz type experiment .

Region A
The beam current increases with voltage following a diode characteristic; some electrons are scattered elastically and will reach the collector ring, the current rising with accelerating potential as shown by the broken line.

Region B
The increase in gradient between regions A & B corresponds to the onset of non-elastic collisions and excitation of the gas atoms; the foot of the curve at 1 represents the critical voltage at which these first occur and corresponds to the first energy level 2¹S above the unexcited "ground state" 1¹S.

In an ideal experiment, the collector current would increase abruptly at 1, but because of the range of energies present in the electron beam due to the nature and temperature of the cathode, the increase is more gradual, reaches a maximum and then falls. This is partly due to the residual energy of the electrons after collision also increasing so that capture by the collector is lessened, and because the fraction of excitations per collision tends to fall off once the critical potential has been exceeded.

Region C & D
In these regions the colliding electrons undergo a similar process to that described in B, the increases in gradient representing the onset of further excitations corresponding to other energy levels within the atom, whilst the decreases are caused by fewer exciting collisions and a smaller number of captures of the "re-bounding" electrons because of their higher residual energies.

Region E
Beyond region D, the gradient continues to increase rapidly because of the onset of ionization which process itself leads to liberation of more electrons as well as positive ions.

That the latter are produced can be established by reversing the polarity of the collector-ring with respect to the anode; with this arrangement, a measure of the ionization potential can be made.

Although nine critical potentials are listed in Table 1, one of which is the ionization potential, the energy differences between some levels are so small that the recording of the difference is "swamped" by the variations in emission velocity of the electrons; transitions from the ground state 1¹S to 2¹S, 2³P, and 2¹P levels may be expected to appear as one potential as do those to 3³S, 3¹S, 3³P and 3¹P levels.

*From Pasco Notes

3.2 Apparatus & Equipment

Apparatus

Figure 5: Frank-Hertz Helium apparatus and electrical connections.

Equipment

1. Pasco (TEL 533) Helium filled tube
2. Filament Supply, DC power supply to furnish filament current, 2-3 V, 1-1.2 A
3. I_f, DC ammeter to measure filament current, 2 A
4. V_A Supply, DC power supply to furnish accelerating voltage, 0 - 45 V
5. I_A, DC microammeter to measure anode current, 200 μA
6. I_C, picoammeter to monitor collecting ring current; internal architecture requires one terminal at earthed ground
7. Computer with A-D DAQ board and installed LabView software

3.3 Precautions

Personal
Any glass tube, as used here, is inherently dangerous if it breaks.

Apparatus
Do not allow filament current, If, to exceed 1.3 A. Do not allow accelerating voltage, V_A, to exceed 35 V. Try to protect the microammeter, the I_A meter, from any inadvertent gross overlead, which would destroy it. Normally, one should expect I_A to not exceed 100 μA.

3.4 Procedure

Figure 6: Experiment Control Panel

Open the Frank-Hertz.vi LabView program. Set the apparatus switch on the control panel to the He experiment.

Information about the control panel and the picoammeter setup is the same as described in Section 2.4.

Experimental measurements.
For this experiment the potential difference between the anode and the loop should be about +1.500V.

Adjust the filament supply so the filament current, I_f, is 1.05 - 1.10 A. The anode current, with no accelerating voltage (V_A = 0), should be 10-50 μA. Whether or not the first minimum, at V_A = V₂ = 18-19 V, is distinctly pronounced, depends on tube conditions, as determined by I_f, for example. Thus, some adjustment of I_f may be needed to obtain satisfactory data. After any adjustment of I_f, the filament will need a few moments to warm up or cool down before any measurements are taken.

Data sets should be taken for the entire range (at the 200nA setting) as well as in the area where the first three minima occur (at the 20nA setting). Also, keep a record of the slowly varying I_A and record I_f.

This completes data taking.

Plots of experimental results.
Present the results in the form of two plots. One is a plot of I_C versus V_A, showing the three minima.

The initial sharp increase in collector current is not associated with a minimum and is rather ambiguous. Make a semi-log plot of I_C versus V_A, with I_C on the log axis. Cover only the region where I_C is small, but including enough range to show the abrupt initial increase in I_C at V_A = V₁.

Interpretation of experimental results.
From the plots made in part (2), estimate the voltages at which abrupt increases in collector current appear, V₁ .. V₄.

These abrupt increases in collector current signify the onset of atomic processes in which the He atom atoms absorb energy from the electrons, i.e., excitation or ionization. The resultant low energy electrons are attracted to the collector loop.

The absolute values of the voltages V₁ .. V₄ lack significance due to contact potentials in the circuit. Moreover, the resolution of the apparatus is not good enough to distinguish between closely spaced atomic energy levels. Qualitative interpretation of the data in terms of the existence of multiple excited states of the He atom and ionization is possible.

Make some effort to qualitatively connect the results of this part of the laboratory with the spectral lines from He observed in another part of the laboratory.

School of Physics at Georgia Tech 837 State Street, Atlanta, GA 30332-0430 USA, Phone:(404) 894-5201, Fax:(404) 894-9958