Neon, Argon, and Mercury were tested in three independent experiments. Monatomic gases were used in order to prevent molecular transitions. If a molecular transition were to occur, it is likely that some of the energy lost in the inelastic collisions would results from molecules separating into singular atoms, thus complicating the analysis. A general circuit diagram for the experimental setup is shown in Figure 1, containing all the elements previously discussed. Figure 2 shows the specific circuits used in each experiment. They are all relatively similar, save a few specific modifications. Mercury is the only element for which a heating chamber is required, since it is a liquid at room temperature. Since Mercury is a liquid at room temperature, the heating chamber allows the Mercury to undergo a phase transition so that it is in a gaseous state. Once Mercury is in a gaseous state, electrons can collide with individual atoms, thus it becomes usable in this study. The mean free path, \(\lambda\), is dependent on the cross section, \(\sigma\), of an interaction and the density, \(N\). For mercury, \(\lambda\) can be approximated using Eqn 1 \cite{Rapior_2006}.

Thus by varying temperature and vapor pressure, the distance an electron travels before interacting with an atom will change.

For all elements, constant current/constant voltage power supplies with adjustable voltages were used so that \(U_{1}\), \(U_{2}\), and \(U_{3}\) could be manipulated. Once the optimal settings were found for each element, \(U_{1}\) and \(U_{3}\) were set at a constant value, and \(U_{2}\) was increased incrementally. In order to obtain the resolution needed to see the complicated shape of the Franck-Hertz curve, the anode current was sent through a current preamplifier which converted current to an output voltage. For Argon, the preamplifier was set to convert current to output voltage with sensitivity \(50\frac{nA}{V}\). For Neon, the preamplifier was set to convert current to output voltage with sensitivity \(2\frac{nA}{V}\). The output voltage from the current preamplifier and the accelerating voltage were connected to two separate digital multimeters. Data was obtained for the monatomic gases using a graphing software called DANA, which is directly linked to the output of the Keithley 2100 multimeter (measuring \(V_{acc}\)) and the Keysight 34465A multimeter (\(V_{out}\)). Not only was the current preamplifier introduced in the experimental setup for Neon and Argon in order to convert current to voltage but it was also used to reduce noise. Since the output of the current preamp was very noisy in the absence of a filter, a basic lowpass filter was introduced to remove frequencies above \(30Hz\). While some of this fine structure is clearly visible in the collected data, not enough data was collected for the observed fine structure to be quantifiable.