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

6.5 x 10^32 eV

Step-by-step 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-(v^(2))/(c^(2))}}`

`E=\frac{m_(0)c^}2}{\sqrt{1-(c^(2))/(4c^(2))}}`

`E=\frac{2m_(0)c^}2}{√(3)}`

`E=(2*0.001*9*10^(16))/(1.732)`

`E=1.04*10^(14)J`

Convert Joule into eV

1 eV = 1.6 x 10^-19 J

So,
`E=(1.04*10^(14))/(1.6*10^(-19))=6.5*10^(32)eV`