Question on relativity An electron rest mass 0511 MeVc2 has

Question on relativity

An electron (rest mass = 0.511 MeV/c^2) has a total energy of 10.00 MeV. What is the speed of this electron? 0.9959c 0.9987c 0.9991c 0.9995c 0.9999c

KE of electron in motion = 10 MeV

Mass of electron in motion = 10/931 amu

since 1 amu = 931MeV

1 amu = 1.67*10^-27 kg

Mass of electron in motion = 10*1.67*10^-27 /931 kg

Me = 1.79*10^-29 kg

me = 9.1*10^-31 kg

from theory of relativity

Me = me/(sqrt(1 - (v/c)^2))

1.79*10^-29 = 9.1*10^-31/sqrt(1 - v^2/(9*10^16))

v = 2.99612*10^8 m/sec

v = (2.99612/3)c = 0.9987 c