deletions | additions       diff --git a/Determining_the_unknown_element_is__.tex b/Determining_the_unknown_element_is__.tex  index 0606c83..75f3fd1 100644  --- a/Determining_the_unknown_element_is__.tex  +++ b/Determining_the_unknown_element_is__.tex 
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Determining the unknown element is a fairly straightforward process, since our plot of spectral distribution has already been calibrated. From Figure~\ref{fig:Unknown_Sample} we find that spectral distribution appears to have two photopeaks. Gaussians were fit to the plot of observed spectral distribution, to obtain a photopeak height of $0.53655 \pm 7.11 \cdot 10^{-5} \textrm{ MeV}$ for the first peak, and a height of $1.2791 \pm 0.000406 \textrm{ MeV}$ for the second peak. It is important to note that a Gaussian curve was fit to the observed data because there is fluctuation in the height of the voltage pulse produced by a gamma ray, which results in a broadening of the photopeak. Thus, a Gaussian is believed to be the best fit for our data. Furthermore, the full width half maximum can be found from the Gaussian fits, and is a good measure of the resolution of the instrument. We then referred to the Smith College Physics radiation safety protocols, which contained information on what radioactive materials the school possessed. There were five sources that the sample could have been, namely, Cesium-137, Cobalt 60, Sodium 22, and Strontium 90. Out of the five potential sources, the spectral distribution obtained from the multi-channel analyzer seemed to match most closely to the spectral distribution of Sodium-22, both qualitatively and quantitatively. Figure ~\ref{fig:sodium_22} shows the known spectral distribution for Sodium-22. When compared to Figure ~\ref{fig:Unknown_Sample}, we can see that the both appear to have two peaks, and those peaks are similar shape. Thus we conclude our observed data qualitatively matches the known spectral distribution for Sodium 22. . Both the observed distribution and the known distribution appear to have two photopeaks. The expected value for Sodium-22's two peaks is $.5110034 \textrm{ KeV}$ and $1.2745 \textrm{ KeV}$ respectively. \cite{IAEA2007}  Our observed values are not consistent within uncertainty of the expected values of Sodium-22, however, the percent error between the expected and observed values is very slight ($5\%$ for the first peak and $0.36\%$ for the second peak) , thus will uphold that we have correctly determined the mystery sample. Furthermore, when compared to the expected photopeak values of the other possible elements the discrepancy between expected and observed values was far larger.