You are given a 1.5 kg sample. Using a high-purity germanium (HPGe) detector to measure the gamma-ray spectrum from this sample, you collect data from this sample for one hour. 1. Your detector collects data in the energy range from 100 keV to 3 MeV. If your sample contains Cs-137, at what gamma-ray energy should you expect to see a significant peak - an excess count rate associated with a gamma-ray decay coming from the Cs-137 contained in your sample? (5pts) 2. If you measure 137 counts total in the Cs-137 peak - integrated over the full Gaussian distribution - what is the uncertainty on this measurement? (5pts) HINT: Recall the relationship between counts measured and standard deviation, or uncertainty, from counting statistics. 3. From your 1-hour measurement, the Cs-137 peak contains 137 counts, but this is after subtracting the background counts under that peak. In the raw spectrum you collect, you actually measure 649 counts in the window around your Cs-137 peak. The rest of the counts are considered detector background, meaning this background is not directly attributed to other sources. 3.a. Where is the background in your spectrum coming from? (5pts)