How Can You Solve Compton Effect Homework Questions on X-ray Scattering?

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The discussion focuses on three homework questions related to the Compton effect and X-ray scattering. The first question involves calculating the energy of a recoiling electron after X-rays of 543 keV undergo Compton scattering with a shift of 3.83x10^-13 m. The second and third questions ask for the maximum fractional energy loss for gamma rays of 0.491 MeV and 0.778 MeV, respectively, when scattered from free electrons and protons. Participants suggest using the Compton shift equation and the energy-wavelength relationship for solving these problems. Concerns are raised about the validity of the first problem, noting that the scattering value appears incorrect as it should result in an increase in wavelength.
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I have 3 homework questions that I need help with:

Q1 X-rays having an energy of 543 keV undergo Compton scattering from a target. The resulting Compton shift is 3.83x1E-13 m. Find the energy of the recoiling electron. (units: keV)


Q2 Find the maximum fractional energy loss for a 0.491 MeV gamma ray that is Compton scattered from a free electron.


Q3 Find the maximum fractional energy loss for a 0.778 MeV gamma ray that is Compton scattered from a free proton.

As far as these questions go, the only thing I can think of doing is somehow manipulating the compton shift equation

delta λ =h/MeC (1-costheta)

or should I use the equation E=hc/λ?

Any help with these problems is very appreciated. Also, if I'm not in the correct forum, please direct me to the correct one.

Thanks.
 
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In 1st problem you have given scatter value (3.83*10-13 m) which is less value compare to incident wavelength:)that i have calculated (3.6*10-12m). According to compton effect wavelength should increas after scattering hence problem is wrong:-)
 
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