(a)Calculate the wavelength (in m) of a photon that has the same momentum as a proton moving at 4.11% of the speed of light.
(b)What is the energy of the photon in MeV?
(c)What is the kinetic energy of the proton in MeV?
a)
from De brogkie hypothesis
L = h / mv
L = 6.636*10^-34 / ( 1.67*10^-27* 0.0411* 3*10^8)
L = 3.22*10^-14 m
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b)
E = h c / L = 6.636* 10^-34 * 3*10^8 / ( 3.22*10^-14* 1.6* 10^-13)
E = 38.61 MeV
=======
c)
as we know
L = h / sqrt ( 2 m E)
E = 0.5( h/ L) ^2 / m
E = 0.5* (6.636*10^-34 / 3.22*10^-14)^2 / ( 1.67*10^-27)
E = 0.795 MeV
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Comment in case any doubt, will reply for sure.. Goodluck
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