91Ó°ÊÓ

The given data can be listed below,

• Speed of electron is $99\%$of speed of light i.e., $v=0.99c$

Rest mass, also known as invariant mass, describes the fascinating behaviour of objects travelling at relativistic speeds. A massless particle possesses rest mass energy, which allows it to move.

The kinetic energy of the particle is given by,

$K.E=\mathrm{γ}m{c}^2-m{c}^2$

Here, $m{c}^2$is the rest mass energy of the particle and $\mathrm{γ}$is the relativistic factor whose value is,

$\mathrm{γ}=\frac{1}{\sqrt{1-{\left(v/c\right)}^2}}$.

The value of $\mathrm{γ}$is given by,

$$\begin{gathered} \mathrm{γ}=\frac{1}{\sqrt{1-{\left(0.99c/c\right)}^2}} \\ =7.09 \end{gathered}$$

Substitute all values in the kinetic energy equation.

$$\begin{gathered} K.E=7.09m{c}^2-m{c}^2 \\ =6.09m{c}^2 \end{gathered}$$

The ratio of kinetic energy with rest mass energy is given by,

$$\begin{gathered} \frac{K.E}{m{c}^2}=\frac{6.09m{c}^2}{m{c}^2} \\ =6.09:1 \end{gathered}$$

Thus, the ratio of kinetic energy and rest mass energy is $6.09:1$.