91影视

The particle鈥檚 momentum magnitude is mc.

The Lorentz factor depends only on velocity and not on the particle鈥檚 mass and it is expressed as

$\mathit{纬}\mathbf{=}\frac{\mathbf{1}}{\sqrt{\mathbf{1}\mathbf{-}{\mathbf{尾}}^{\mathbf{2}}}}$

$\mathbf{尾}$is called the speed parameter which is ratio of speed of particle to speed of light.

.$\mathbf{尾}\mathbf{}\mathbf{=}\mathbf{}\mathbf{V}\mathbf{/}\mathbf{C}$

It is given that a particle鈥檚 momentum magnitude is mc . The relativistic momentum relation is given by

$p=纬mv$

Putting the given momentum in above expression, we get

$$\begin{gathered} mc=纬mv \\ 纬v=c \\ 纬\frac{v}{c}=1 \\ 纬尾=1 \end{gathered}$$ 鈥� (1)

We know that the Lorentz factor depends only on velocity and not on the particle鈥檚 mass and it is expressed as

$纬=\frac{1}{\sqrt{1-{尾}^2}}$

Inserting this in equation (1), we get

$$\begin{gathered} \frac{尾}{\sqrt{1-{尾}^2}}=1 \\ {尾}^2=1-{尾}^2 \\ 尾=\frac{1}{\sqrt{2}} \\ =0.707 \end{gathered}$$

Hence the value of $尾$is, 0.707.

Putting the value of$尾$ in the equation (1),

$$\begin{gathered} 纬=\frac{1}{尾} \\ =\frac{1}{0.707} \\ =1.414 \end{gathered}$$

The value of $纬$is, 0.414.

The relativistic kinetic energy relation is given by

$$\begin{gathered} K=\left(纬-1\right)m{c}^2=\left(纬-1\right)E_o \\ \frac{K}{E_o}=纬-1 \end{gathered}$$

Substitute all value in the above equation

$$\begin{gathered} \frac{K}{E_o}=1.414- \\ =0.414 \end{gathered}$$

Hence the value of $\frac{K}{E_o}$is,0.414 .

And thus, all the required values are determined.