Problem $8(10pts)$ : All $K^0$ particles have mass of $m_{K^0}=8\mathrm{.}85{10}^{-28}kg.$ The $K^0$ particle is unstable and decays to a pair of ${}^0$ particles $($this reaction is denoted $K^0{}^0{}^0).$ If the $K^0$ is at rest when it decays, the kinetic energy of each ${}^0$ particle is the same $K=1\mathrm{.}82{10}^{-11}$ Joules. $[$Hint: use only relativistic equations in this problem.$]$

a$)(2$ pts $)$ What is the rest energy of the $K^0$ particle?

b$)(3$ pts$)$ What is the total energy of each ${}^0$ particle?

c$)(3$ pts $)$ What is the mass of the ${}^0$ particle?

d$)(2$ pts$)$ What are the rest energies of the $K^0$ and ${}^0$ particles, expressed in MeV $($millions of electronvolts$)?$

$1\mathrm{.}0V=1\mathrm{.}6*10-19J$