Question

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

Answer 1

Step 1. Given data:

Rest mass $\left(m_0\right)=$0

Let $v=$ 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,

$m=\frac{m_0}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$, 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

$\Rightarrow \sqrt{1-\frac{v^2}{c^2}}=0$, squaring both sides, we get

$$\begin{gathered} 1-\frac{v^2}{c^2}=0 \\ or\frac{v^2}{c^2}=1 \\ \Rightarrow v=c \end{gathered}$$

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.