A crucial step in obtaining accurate values for the energy loss from Compton scattering is to properly calibrate the detection system, comprised of a photomultiplier tube (PMT) coupled to a multi-channel analyzer (MCA). Recall that the PMT converts an incident photon into an electron shower, yielding a pulse of electrons that is proportional to the energy of the photon. The MCA then converts the pulse height into a bin number, so that the bin number is a linear function of the photon energy. You will calibrate the detection system using two sources: 133Ba and 137Cs which emit gamma rays of energy EB = 0.3560 MeV and EC = 0.6617 MeV, respectively.
1. Suppose that the peaks in the gamma-ray distributions occur at bin number B=0.348 for _{}^{133}\textrm{Ba} and bin number C=0.609 for _{}^{137}\textrm{Cs} . The equation relating bin number (#) to energy can be written as E=a+b*#. If b is known, the parameter a can be found from either energy, e. g. a = E_{B} - b*B. For your values of B and C, calculate the parameter b = MeV/#.
2. Now assume that the parameters for your energy calibration are a = -35.635 MeV and b = 1.1365 MeV/#. If a peak in the scattered gamma rays occurs in bin # = 502, the corresponding gamma ray energy is E_{P} = MeV.