Question

What is the total energy of a particle with a rest mass of 1 gram moving with half the speed of light? 1 eV = 1.6 x 10^-19 J. Answer in units of eV.

Answer 1

Answer:

6.5 x 10^32 eV

Explanation:

mass of particle, mo = 1 g = 0.001 kg

velocity of particle, v = half of velocity of light = c / 2

c = 3 x 10^8 m/s

Energy associated to the particle

E = γ mo c^2

$E=\frac{m_{0}c^}2}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

$E=\frac{m_{0}c^}2}{\sqrt{1-\frac{c^{2}}{4c^{2}}}}$

$E=\frac{2m_{0}c^}2}{\sqrt{3}}$

$E=\frac{2\times0.001\times9\times10^{16}}{1.732}$

$E=1.04\times10^{14}J$

Convert Joule into eV

1 eV = 1.6 x 10^-19 J

So, $E=\frac{1.04\times10^{14}}{1.6\times10^{-19}}=6.5\times10^{32}eV$