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\textbf{Abstract}
\end{centering}
\begin{centering}
\par We performed
both Doppler and subDoppler spectroscopy on the $5^{2}S_{1/2}$ → $5^{2}P_{3/2}$ transition of rubidium 85
($^85$ Rb) ($^{85}$Rb) and rubidium 87
($^87$ Rb). Using ($^{87}$Rb). We fit the Doppler
spectroscopy, we found spectroscopy curves to Maxwell Boltzmann velocity distributions to determine the
energies temperature of the
transition of cell. We also fit the
subDoppler spectroscopy curves to extract the transition energies and hyperfinestructure of the $5^{2}S_{1/2}$ F=2 ground state
of rubidium 85 to the $5^{2}P_{3/2}$
state, the F=1, F=2, and F=3 excited
state states of
$^{85}$Rb, the $5^{2}S_{1/2}$
F=3 ground state
of rubidium 85 to the $5^{2}P_{3/2}$
state, the F=1 F=2, F=3, and F=4 excited
state states of
$^{85}$Rb, the $5^{2}S_{1/2}$
F=1 ground state
of rubidium 87 to the $5^{2}P_{3/2}$
state, F=0, F=1, and
the F=2 excited
state states of
$^{87}$Rb, and the $5^{2}S_{1/2}$
F=2 ground state
of rubidium 87 to the $5^{2}P_{3/2}$
state. F=1, F=2, and F=3 excited states of $^{87}$Rb. The Our results were not quite consistent with theory within uncertainty, but there are many possible reasons for this slight discrepancy.
Using saturation absorption spectroscopy, we were able to resolve The uncertainty in the
hyperfine structure of each Doppler profile fitting is most likely due to an incomplete model of the
previously mentioned energy levels. Our results again were not quite consistent with theory within uncertainty, but that transmission curve. While we modeled the as a Maxwell Boltzmann Gaussian distribution, the actual curve is a convolution between the six Lorenztian line profiles and the Gaussian distribution. The uncertainty in the hyperfine fitting is likely mainly due to the fact that we modeled our frequency scan as linear but it is not actually linear.
\end{centering}
