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

Answer:

1.3×10³³ eV

Explanation:

Rest mass of particle = 1 gram

Speed of light = c

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

Energy

$E=\frac{m_0c^2}{\sqrt{1-\frac{v^2}{c^2}}}\\\Rightarrow E=\frac{1\times 10^{-3}(3\times 10^8)^2}{\sqrt{1-\frac{0.5^2c^2}{c^2}}}\\\Rightarrow E=\frac{1\times 10^{-3}(3\times 10^8)^2}{\sqrt{1-0.25}}$

Converting to eV

$\frac{1\times 10^{-3}(3\times 10^8)^2}{\sqrt{1-0.25}}\times \frac{1}{1.6\times 10^{-19}}=6.49\times 10^{32}$

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