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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 excitation energy of $19.4993 \pm 0.6$ eV. However, 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}.) \\ When %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.