(a)
Since , Etotal = m*c^2/sqrt (1 - v^2/c^2)
here, m = mass of proton = 1.67*10^-27 kg
c = velocity of light
v = velocity of proton = 0.800c
So,
Etotal = [(1.67*10^-27)*(3*10^8)^2]/sqrt (1 - 0.800c^2/c^2)
Etotal = 2.505*10^-10 J
Since 1 J = 6.242*10^18 eV
So,
Etotal = (2.505*10^-10)*(6.242*10^18) eV
Etotal = 1.564*10^3 MeV
(b)
Since,
Etotal = Ekinetic + E_rest
here, Erest = m*c^2
Erest = (1.67*10^-27)*(3*10^8)^2 = 1.503*10^-10 J
Erest = (1.503*10^-10)*(6.242*10^18) eV
Erest = 9.38*10^2 Mev
So,
Ekinetic = Etotal - Erest
Ekinetic = (1564 - 938) MeV
Ekinetic = 6.26*10^2 MeV
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