Answer
(a) $E = 6700~MeV$
(b) $E = 3.6~MeV$
Work Step by Step
(a) We can find $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-\frac{(0.99~c)^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{0.0199}}$
$\gamma = 7.09$
We can find the proton's total energy:
$E = \gamma ~m~c^2$
$E = (7.09)(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2$
$E = 1.0656\times 10^{-9}~J$
$E = (1.0656\times 10^{-9}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 6.7\times 10^9~eV$
$E = 6700\times 10^6~eV$
$E = 6700~MeV$
(b) We can find the electron's total energy:
$E = \gamma ~m~c^2$
$E = (7.09)(9.109\times 10^{-31}~kg)(3.0\times 10^8~m/s)^2$
$E = 5.81245\times 10^{-13}~J$
$E = (5.81245\times 10^{-13}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 3.6\times 10^6~eV$
$E = 3.6~MeV$
