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\subsection{Neon Experiment}   Using Fig. \ref{fig:NeonAnalysis} and Eq. \ref{eq:lowestlevel}, we plugged in n=0.5 to find the excitation level for each of the linear fits shown in the plot. This generated an excitation energy of $19.4993 $19.50  \pm 0.6$ 0.60$  eV. Since the collisions are quite frequent, this value should correspond to the first excitation level. However, this is not consistent with the first excitation energy level shown on the NIST website (Fig. \ref{fig:NeonEnergyLevels}). One possible reason for such a high value could be due to the high voltage and  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. \\ \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 $10.80  \pm 0.02$ eV. According to the NIST website, the first excitation energy level occurs around 11.6 11.55  eV as shown in \ref{fig:ArgonEnergyLevels}. 11.6eV 11.55eV  does not fall within the range of the experimentally determined lowest excitation level of $10.7991 $10.80  \pm 0.02$ eV. However, it is close. \textbf{sig figs? any other edits?}