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 Ã 10â19 J . Answer in units of eV.

Answer 1

1.3×10³³ eV

Step-by-step explanation:

Rest mass of particle = 1 gram

Speed of light = c

Speed of particle = (1/2)c = 0.5 c

Energy

`E=\frac{m_0c^2}{\sqrt{1-(v^2)/(c^2)}}\\\Rightarrow E=\frac{1* 10^(-3)(3* 10^8)^2}{\sqrt{1-(0.5^2c^2)/(c^2)}}\\\Rightarrow E=(1* 10^(-3)(3* 10^8)^2)/(√(1-0.25))`

Converting to eV

`(1* 10^(-3)(3* 10^8)^2)/(√(1-0.25))* (1)/(1.6* 10^(-19))=6.49* 10^(32)`

∴ Total energy of the particle is 6.5×10³² eV.