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\section{Results}   \subsection{Muon Decay}  \subsubsection{Mean Lifetime}  A plot of data collected over a five day period can be seen in Figure (). Data for a time in the range of $0-12\mu seconds$ was plotted as a histogram with bin size 60 ns. To increase the () accuracy  of our expected mean muon lifetime, a few adjustments were made. First the data was trimmed, which slightly increased our calculated value of (), $\tilde\chi^2$ ,  indicating a () result. It should also be noted (refer to Figure ()) that fewer decays occurred at high time measurements, and thus the uncertainty on these values were higher. Although it was not done for this experiment, it is possible to weight the data points such that the decays that occurred at higher time measurements are less significant. Mean muon lifetime was taken from a best fit plot which had equation of the form: \par The final value was found to be (), which is well within the expected values for both muon decay and antimuon decay, () and () respectively. Though are value for lifetime matches the known values within uncertainty, it is still important to note that some experimental uncertainty is expected, since energy parameters were set for muon detection. Though this was done in order to eliminate events that were not assumed to be associated with muon decay, it is entirely possible that some muons escaped detection due to the () parameters.   \subsubsection{Charge Density}  Since we know that both have positive and negative muons contribute to the mean muon lifetime, it is also important to have some sort of quantantative understanding of the ratio, $\rho$ of muons to antimuons is. We can calculate $\rho$ via Equation ()   \begin{equation}  \rho=-\frac{\tau^{+}}{\tau^{-}}(\frac{\tau^{-}-\tau_{obs}}{\tau^{+}-\tau_{obs}})=\frac{N^{+}}{N^{-}}  \end{equation}  Where $\tau^{+}$ is the known value of the mean lifetime for an antimuon, $\tau^{-}$ is the known value of the mean lifetime for a muon, $2.03 \mu seconds$,  and $\tau_{obs}$ is the value (), $2.04\pm0.04 \mu seconds$,  taken from the best fit of our data. \subsection{Gamma Ray Spectroscopy}  \subsubsection{Dertermining the Unknown Sample}  In order to determine what element the unknown sample was, we kept all the same settings from the calibration trial, and kept the calibrations the same in order to find the peak values of the unknown sample. We placed the unknown sample into the scintillator at the fifth slot from the top and the sample was within an old film container.Just like Cesium-137 and Cobolt, the gamma ray is detected from converting visible light into a voltage pulse (as seen in Figure \ref{Figure:Sodiumsetup}).  The sample ran for $3670$ seconds Live Time. The difference between Live Time and Real Time is that as the program is producing the spectrum, there is a slight lag as it processes the data. So, the Live Time is the actual time the data is being recorded. By keeping the calibrations from trials 1 and 2, we were able to run the sample and have the data in Energy versus intensity instead of bins versus intensity. Beause we know the energy of the peaks it made it simple to find the element of the unknown sample. From the Smith College Physics radiation safety protocols version 5.0, we know that the only radioactive materials the sample could be are Cesium-137, Cobalt 60, Sodium 22, and Strontium 90. This reduced the error in our unknown sample because that left us with only four possible elements. As you can see in Figure \ref{fig:Unknown_Sample}, there are two peaks. After fitting gaussians to each peak (using Igor Pro), the first peak is at $0.53655 \pm 7.11 \cdot 10^{-5} \textrm{ MeV}$ and the second is at $1.2791 \pm 0.000406 \textrm{ MeV}$.