What is the appropriate gain for the MCA amplifier in this scenario?

[dagg3r]

A radioactive material emits 2 gamma rays with 2 energies 50 keV and 200 keV with equal probabilities the detector system has a quantum efficiency of 100% and 50% respectively at these 2 energies and the pulse heights are 1.0 mV and 4.0mV respectively. The pulses are input into a 512 channel, 10 V lfull scale, MCA. The total system has an energy resolution of 20 keV.

Suggest an appropriate gain of the MCA amplifier


i sketched the displayed spectrum... also looking at the solutions they somehow got a gain of 2*10^3 with the pulse height of 4.0 mV at a channel 409 corrresponding to 8 V.

any ideas how htey got that gain and the channel number corresponding to the pulse height?

i tried fiddling round with the formulas given of
energy resolution = (FWHM / pulse height at centre of peak) * 100%
no luck.. somehow they got a gain of 2*10^3 for a plot that is num of counts vs channel number...

hope you guys know

 

[Gokul43201]

I don't see why the gain chosen shouldn't just follow from the largest detected signal (4mV) and the FS value (10V). Since the MCA gain on a spectrometer is usually selected on a dial, you have a limited number of options. A gain of 2000X will amplify a 4mV signal to 8V (80% of FS). A higher gain setting (like 4000X or 5000X) would take the high energy peak off-scale.