Question

How fast must an electron move so that its total energy is 17% more than its rest mass energy? Give your answer as a fraction of c. Express your answer using three significant figures.

Answer 1

The rest energy of the electron is

Eo= m_oc²

We calculate energy

In this case we must include the relativistic correction

E= m c²/ sqrt ( 1- (u/c)²)

They tell us that energy is 17% = 0.17 greater than the rest energy

E = Eo + 0.17 Eo = 1.17 Eo

m_oc²/ sqrt ( 1- (u/c)²) = 1.17 m_oc²

1/sqrt ( 1- (u/c)²) = 1.17

1 = 1.17²( 1- (u/c)²)

1/1.17² = 1 – (u/c)²

(u/c)²= 1 – 0.7305 = 0,2695

u = c sqrt (0.2695)

u = 0.519 c