Answer
(a) $K = 0.00512~MeV$
(b) $K = 9.39~MeV$
(c) $K = 37.6~MeV$
Work Step by Step
(a) We can find the kinetic energy when $\gamma = 1.01$:
$K = (\gamma-1) ~mc^2$
$K = (1.01-1) ~(9.109\times 10^{-31}~kg)(3.0\times 10^8~m/s)^2$
$K = 8.1981\times 10^{-16}~J$
$K = (8.1981\times 10^{-16}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$K = 5.12\times 10^{3}~eV$
$K = 0.00512\times 10^{6}~eV$
$K = 0.00512~MeV$
(b) We can find the kinetic energy when $\gamma = 1.01$:
$K = (\gamma-1) ~mc^2$
$K = (1.01-1) ~(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2$
$K = 1.503\times 10^{-12}~J$
$K = (1.503\times 10^{-12}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$K = 9.39\times 10^{6}~eV$
$K = 9.39~MeV$
(c) We can find the kinetic energy when $\gamma = 1.01$:
$K = (\gamma-1) ~mc^2$
$K = (1.01-1)(4)(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2$
$K = 6.012\times 10^{-12}~J$
$K = (6.012\times 10^{-12}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$K = 3.76\times 10^{7}~eV$
$K = 37.6\times 10^{6}~eV$
$K = 37.6~MeV$
