Question

What is the total energy of an electron when its momentum is 10 times its rest mass multiplied by the light velocity?

Answer 1

For this problem we use formula

$$E=c\sqrt{m_0^2c^2+p^2}$$

initial condition

$$p=10m_0c$$

then

$$E=m_0c^2\sqrt{11}$$

rest energy for electron

$$E_0=m_0c^2=0.511 (MeV)$$

then

$$E=E_0\sqrt{11}=0.511*\sqrt{11}=1.695 (MeV)$$

In joules it

$$E=1.695 \cdot 10^6 \cdot 1.6 \cdot 10^{-19}=2.711\cdot 10^{-13} (J)$$