Homework$-$Week $14($show your work$)$

$($P$13)(15$ points$)$

The point of this question is to compare rest energy and kinetic energy at high speeds. An alpha particle $($a helium nucleus$)$ is moving at a speed of $0\mathrm{.}9993$ times the speed of light. Its mass is $6\mathrm{.}4{10}^{-27}kg.$

$($a$)$ What is its rest energy?

$($b$)$ Is it okay to calculate its kinetic energy using the expression $\frac{1}{2}m{v}^2?$

$($c$)$ What is its kinetic energy?

$($d$)$ Which is true? A$.$ The kinetic energy is approximately equal to the rest energy. B$.$ The kinetic energy is much bigger than the rest energy. C$.$ The kinetic energy is much smaller than the rest energy?