Question

Calculate the kinetic energy of a proton whose velocity is 0.8c.

Answer 1

The relativistic kinetic energy of a proton is given as follows:

$$E_k =\frac{m c^2}{\sqrt{1- v^2/c^2 }}-m c^2= mc^2\left( \frac{1}{\sqrt{1- v^2/c^2 }} - 1\right)$$

where $mc^2 = 938\space MeV$ is the rest energy of a proton, $v = 0.8c$ is the speed of the proton, and $c$ is the speed of light. Thus, obtain:

$$E_k = 938\space MeV\left( \frac{1}{\sqrt{1- 0.8^2c^2/c^2 }} - 1\right) \approx 625.3\space MeV\approx 10^{-10}J$$

Answer. $10^{-10}J$.