How fast must an electron move so that its total energy is 1

How fast must an electron move so that its total energy is 13% more than its rest mass energy? Give your answer as a fraction of c.

Solution

Rest mass energy = m0 c^2

and total energy = m c^2

and m = mo / sqrt(1 - (v/c)^2)

and total energy is 13% more than its rest energy.

total energy = 1.13 (rest mass energy )

1 / sqrt(1 - (v/c)^2) = 1.13

1 - (v/c)^2 = 0.783

v/c = 0.466

v = 0.466c .........Ans