Question

At what speed, as a fraction of c, must an electron move so that its total energy is 10% more than its rest mass energy?

Short answer

The speed of electron is 0.417c.

Step-by-step solution

Given information

We have given that, total energy of electron is 10% more than its rest mass energy.

Step 1.

As the total energy is 10% more of rest mass energy, we can write it as :

${{\rm Y}}_{p}m{c}^2=\frac{110}{100}m{c}^2$

Here,${{\rm Y}}_p$= Lorentz factor

m = mass of electron

c = speed of light

${{\rm Y}}_p=1.1$

${\rm Y}$

Step 2.

We know that ${{\rm Y}}_p=\frac{1}{\sqrt{1-{\displaystyle \raisebox{1ex}{$v^2$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.}}}$. Substituting this value of ${{\rm Y}}_p$:

$\frac{1}{\sqrt{1-{\displaystyle \raisebox{1ex}{$v^2$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.}}}=1.1$

$v=0.417c$