Answer to Question #88928 in Mechanics | Relativity for Sridhar

Question

What is the total energy of an electron when its momentum is 10 times its it is multiplied by the light velocity (rest mass of electron equals to 9×10^-31 kg)

Answer 1

The total energy of an electron depends on its rest energy and kinetic energy:

$$E=\sqrt{(m_0c^2)^2+(pc)^2}=\sqrt{(m_0c^2)^2+([10m_0c]c)^2},$$

$$E=\sqrt{(9\cdot10^{-31}(3\cdot10^8)^2)^2+([10\cdot9\cdot10^{-31}\cdot3\cdot10^8]3\cdot10^8)^2}=$$

$$=8.14\cdot10^{-13}\text{ J}.$$