Question

1.   Calculate the kinetic energy and momentum of a proton traveling 2.90 𝑥 108 𝑚/𝑠.

Answer 1

The relativistic kinetic energy of a proton is

$K=\frac{1}{\sqrt(1-(\frac{v}{c})^2)} mc^2$

$=\frac{1}{\sqrt(1-(\frac{2.90 \times10^8}{3 \times10^8})^2)} (938 MeV) =3663.5 MeV$

The relativistic momentum of a proton is

$p=\frac{1}{\sqrt(1-(\frac{v}{c})^2)} mv$

$=\frac{1}{\sqrt(1-(\frac{2.90 \times10^8}{3 \times10^8})^2)} (938 MeV/c^2)(\frac{2.90 \times10^8}{3 \times10^8})c$

$=35141.5 MeV/c$