How much work must be done to increase the speed of an electron (a) from 0.18c to 0.19c and (b) from 0.98c to 0.99c? Note that the speed increase is 0.01c in both cases.

Answer 1

Total energy is

E(rest) + E(kin)
= m*c^2/sqrt[1 - (v/c)^2]

Calculate that at each speed and take the difference.

(a) m*c^2/sqrt[1 - .19^2]
- m*c^2/sqrt[1 - .18^2]

= m*c^2[1.01855 - 1.01660]
= m*c^2* 1.95*10^-3

Answer 2

I got 1*10^-16 but what's the unit for my answer? Because the book says 1.0 ke V is the answer for part (a). How do I get there?

Answer 3

You should have got 1.6*10^(-16) as your answer - Which is the value of 1keV.