Optimizing MCA Amplifier Gain for High Energy Resolution: A Case Study

[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

 

[Aaron Barnard]

The gain of the MCA amplifier can be determined by comparing the expected pulse height with the full scale voltage of the MCA. The expected pulse height is calculated by multiplying the energy of the gamma ray (50 keV and 200 keV) with the quantum efficiency of the detector system (100% and 50%).
For the 50 keV gamma ray, the expected pulse height is 50 keV x 100% = 50 mV. For the 200 keV gamma ray, the expected pulse height is 200 keV x 50% = 100 mV. Since the full scale voltage of the MCA is 10 V, the gain of the MCA amplifier needs to be set such that the pulse heights are scaled to the full scale voltage of the MCA.

Therefore, the gain of the MCA amplifier should be set to 10 V / 150 mV = 66.67. To get a more precise answer, the gain can be rounded off to 66.7 or 67.

 

[piercas]

the answer

I would recommend further analyzing the data and calculations used in the case study to understand how they arrived at a gain of 2*10^3 and the corresponding channel number. It is important to have a clear understanding of the equations and assumptions used in order to replicate and validate the results.

One approach could be to analyze the pulse height corresponding to the 200 keV gamma ray (4.0 mV) and use that to calculate the gain needed to achieve a channel number of 409 (8 V) for optimal energy resolution. This could involve using the equation for energy resolution and solving for gain, taking into account the quantum efficiencies at the two energies and the full scale voltage of the MCA.

It is also important to consider any potential sources of error or uncertainty in the measurements and calculations. This could include variations in the quantum efficiencies, pulse heights, or other factors that could impact the final result.

Overall, the key is to thoroughly understand the principles and equations involved in order to accurately determine the appropriate gain for the MCA amplifier in order to achieve high energy resolution.