Explanation

(d) The relativistic kinetic energy of a particle of rest mass $m_{0}$ is given by
$K = \left( m - m_{0} \right)\ c^{2}$
$m = \frac{m_{0}}{\sqrt{1 - (v^{2}/c^{2})}},$ where $m$ is the mass of the particle moving with velocity v.
$\therefore K = \left\lbrack \frac{m_{0}}{\sqrt{1 - \left( v^{2}/c^{2} \right)}} - m_{0} \right\rbrack\ c^{2}z$
According to problem
kinetic energy = rest energy
$\therefore\ \ \left\lbrack \frac{m_{0}}{\sqrt{1 - \left( v^{2}/c^{2} \right)}} - m_{0} \right\rbrack = m_{0}c^{2}$
or $\frac{m_{0}c^{2}}{\sqrt{1 - \left( v^{2}/c^{2} \right)}} = 2m_{0}c^{2}\ or\frac{1}{1 - \left( v^{2}/c^{2} \right)} = 4\ or\frac{4v^{2}}{c^{2}} = 3\ $
$\therefore v = \frac{\sqrt{3c}}{2}$