Question

# A particle which has zero rest mass and non-zero energy and momentum must travel with a speed

Open in App
Solution

## Step 1. Given data:Rest mass $\left({m}_{0}\right)=$0Let $v=$ speed of the particle; $c=$ speed of light; $m=$ mass of the particle when it is moving Step 2. Formula used:As we know that the mass of a moving particle is given by the following formula,$m=\frac{{m}_{0}}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$, where all the variables are described above.Step 3. Explanation:Since it is given that the rest mass of the particle is zero, so ${m}_{0}=0$. Putting the value of ${m}_{0}$ in equation, we get$⇒\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}=0$, squaring both sides, we get$1-\frac{{v}^{2}}{{c}^{2}}=0\phantom{\rule{0ex}{0ex}}or\frac{{v}^{2}}{{c}^{2}}=1\phantom{\rule{0ex}{0ex}}⇒v=c$It shows that the speed of the particle is equal to the speed of light.Particle is a photon and it travels with a velocity equal to light in vacuum.Hence, a particle that has zero rest mass and non-zero energy and momentum must travel with a speed equal to the speed of light.

Suggest Corrections
2