An electron has a rest energy of 0.511 MeV.At what speed would its kinetic energy equal 1.022 MeV?
A) 0.866 c
B) 0.942 c
C) 0.888 c
D) 0.971 c
E) 0.500 c

Question

Quizplus · Accepted Answer

We can use the special relativistic equation for the total energy of a particle:

E² = (pc)² + (m₀c²)²

where E is the total energy (kinetic + rest), p is the momentum, m₀ is the rest mass, and c is the speed of light.

At rest, the electron has an energy of E₀ = m₀c² = 0.511 MeV.

When the kinetic energy equals 1.022 MeV, the total energy is:

E = E₀ + K = m₀c² + (γ - 1)m₀c²

where K is the kinetic energy and γ is the Lorentz factor:

γ = 1 / sqrt(1 - v²/c²)

Setting E equal to 1.022 MeV and solving for v, we get:

v/c = sqrt(1 - (m₀c² + K)² / (E₀ + K)²) = 0.942

Therefore, the answer is B) 0.942 c.

An Electron Has a Rest Energy of 0