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(A) The rest mass energy of an electron is $E_e = 0.51 \, MeV$ and that of a positron is $E_p = 0.51 \, MeV$.When they annihilate, the total energy re

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$0.012 \, \mathring{A}$

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(A) The rest mass energy of an electron is $E_e = 0.51 \, MeV$ and that of a positron is $E_p = 0.51 \, MeV$.When they annihilate, the total energy released is $E_{total} = E_e + E_p = 0.51 \, MeV + 0.51 \, MeV = 1.02 \, MeV$.Converting this energy to Joules: $E_{total} = 1.02 	imes 10^6 	imes 1.6 	imes 10^{-19} \, J = 1.632 	imes 10^{-13} \, J$.The wavelength $\lambda$ of the produced gamma-rays is given by $\lambda = \frac{hc}{E_{total}}$.Substituting the values: $\lambda = \frac{6.63 	imes 10^{-34} 	imes 3 	imes 10^8}{1.632 	imes 10^{-13}} \, m$.$\lambda \approx 1.218 	imes 10^{-12} \, m = 0.01218 	imes 10^{-10} \, m = 0.012 \, \mathring{A}$.

The rest mass of an electron as well as that of a positron is $0.51 \, MeV$. When an electron and a positron annihilate, they produce gamma-rays of wavelength(s):

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