In 1914, James Franck and Gustav Hertz performed experiments which demonstrated the discrete atomic energy levels of the electrons in various elements. You will observe these levels in Mercury vapor contained in a Franck-Hertz tube that is heated in an oven. The diagrams for the Franck-Hertz tube to be used is shown below.
Inside the tube, a variable voltage between two grids (g1 and g2) accelerates electrons boiled from a cathode (f and fk) through the Hg vapor. The kinetic energy of the electrons is determined from the potential difference between the grids. An anode collector plate (A) is located beyond the second grid (g2) and collects some of these electrons, which is measured as a current (I) in an ammeter or current amplifier.
Most of the electrons which collide with the Hg atoms undergo an elastic collision and are merely deflected. However, if the electron KE is precisely the same as the difference between two atomic energy levels in the Hg, then that energy can be absorbed by the Hg atom and the electron is virtually stopped in a totally inelastic collision. This effect is seen as a drop in the current to the collector plate. Hence, one can see a drop in the collector current as the grid potential approaches a value in which the electron KE matches this atomic transition. These are called critical potentials.
As the grid potential is increased further, the collector current will begin to rise again but another drop will be seen as the electron KE approaches twice the previous value. This occurs because some of the electrons are completely stopped through two inelastic collisions. This process repeats indefinitely and the effect can be seen in the plot of collector current vs acceleration potential shown below.
Follow the instruction sheet carefully when setting up the experiment. The collector current will be measured with a sensitive ammeter or current amplifier. Vary the grid to grid voltage (U2) from zero to about 40 volts and look for clear indications of the dips in the collector current. (Warning: If the collector current rises sharply, turn off the grid voltage immediately and increase the oven temperature.) In order to obtain good results, you may need to adjust the oven temperature (via the Variac voltage) and/or the space voltage (U1) between the cathode and first grid.
Record the collector current at .5 V intervals. In the region of the peaks, take readings at .1 V intervals. (You may wish to hunt for the precise voltage at which the current begins to drop and specifically note that value.) Continue until you have 4 distinct peaks. Plot I vs U2 and determine the voltages at each peak in the curve. Find the difference in voltage between each of the peaks and compare them. Compare these results to the dominant atomic energy level differences in Hg by consulting the emission and absorption spectra lines listed in the CRC Handbook. Can you identify a particular atomic transition line? Discuss your conclusions, including an error estimation in determining the electron KE energy from your data and the effect of the thermal motion of the Hg atoms at approximately 200 oC.
