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\subsection{Neon Experiment}   Using \ref{fig:NeonAnalysis} and Eq. \ref{eq:lowestlevel}, we plugged in x to be 0.5 to find the excitation level for each of the linear fits shown in the plot. This generated a an  excitation energy of $19.4993 \pm 0.6$ eV. This has to be the first excitation level because we derived Eq. \ref{eq:lowestlevel} by setting $E_a$ equal to the lowest energy level. However, this is not consistent with the first excitation energy level shown on the NIST website. (Fig. \ref{fig:NeonEnergyLevels}.) However, this inconsistent value could be due to the high voltage preamp damage after the failure to make a connection between the filament and accelerating voltage. In our experiment, we debugged our system and found that the gain of the high voltage supply was actually times 17V instead of 20V. After compensating for the true gain, we found the excitation level of neon to occur around $16.66 \pm 0.51$ eV. This value is much closer to the first excitation level of neon according the the NIST website.  \\ %actually Eq1. only assumes that Ea corresponds to the difference between two energy levels in the Ne atom. It doesn’t have to be the first excitation level, but would normally be so if collisions are very frequent. There are Ne energy levels in the 19.5 ± 0.6 eV range. In this case, however, this could be due to I think this could be because after the damage done to the HV preamp after the failure to include a connection between the filament and the accelerating voltage, the gain was only x17 rather than x20. So then you would think the energy difference was 19.5 V, but it would really be (17/20)(19.5) = 16.6 V.  %When we subtract the background from Fig. \ref{fig:NeonAnalysis}, the first excitation level turns out to be quite high. And this has to be the first excitation level because we derived Eq. \ref{eq:lowestlevel} by setting $E_a$ equal to the lowest energy level. So, we conclude that we our data does not match the first excitation level of around 16.62eV. \\  \subsection{Argon Experiment}  Using \ref{fig:ArgonAnalysis} and Eq. \ref{eq:lowestlevel}, we plugged in n=0.5 into the cubic fit to find the lowest excitation energy for argon just like what we did for neon. The number we got appeared to be $10.7991 \pm 0.02$ eV. According to the NIST website, the first excitation energy level occurs around 11.6 eV as shown in \ref{fig:ArgonEnergyLevels}. 11.6eV does not fall within the range of the experimentally determined lowest excitation level of $10.7991 \pm 0.02$ eV. However, it is close.