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\section{Conclusion}  Our experimental data is consistent with We have presented an undergraduate experiment aimed at designing and understanding  the energy levels from physics and math behind  the NIST website Franck-Hertz experiment based on our textbook \cite{Melissinos_2003}. We studied the Franck-Hertz Experiment  for two different atoms: neon and argon. We found  the argon atoms. However, it differs lowest excitation energy level  for neon atoms. Our experiment has a precise method that corresponds with to occur at $19.4993 \pm 0.6$ eV. Whereas, we found  the method used in our textbook \cite{Melissinos_2003}. lowest excitation energy level for argon to occur at $10.7991 \pm 0.02$ eV. The argon data was shown to be the most precise measurements.  We conclude that our argon experiment is precise and accurate. However, our neon experiment has there must have been  some systematic errors. error for the neon experiment.