Answer
$E = 942~MeV$
Work Step by Step
In part (a) we found that the Compton wavelength for a proton is $~~1.32\times 10^{-15}~m$
We can find the energy of a photon with this wavelength:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.63\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{1.32\times 10^{-15}~m}$
$E = 1.507\times 10^{-10}~J$
$E = (1.507\times 10^{-10}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 9.42\times 10^8~eV$
$E = 942~MeV$
