An electron is accelerated from rest through a potential difference of 1.02 MeV.If the rest energy of the electron is 0.51 MeV,how fast is the electron moving?
A) 0.57 c
B) 0.30 c
C) 0.67 c
D) 0.90 c
E) 0.94 c

Question

Quizplus · Accepted Answer

From the conservation of energy, we know that the kinetic energy gained by the electron is equal to the potential energy lost. Therefore:

K = U = 1.02 MeV - 0.51 MeV = 0.51 MeV

To find the velocity of the electron, we use the formula for relativistic kinetic energy:

K = (γ - 1)mc²

where γ is the Lorentz factor and mc² is the rest energy of the electron.

Substituting the values, we get:

0.51 MeV = (γ - 1)(0.51 MeV/c²)

γ - 1 = 1

γ = 2

Therefore, the velocity of the electron can be calculated using the formula for the Lorentz factor:

γ = 1/√(1 - v²/c²)

Solving for v, we get:

v = c√(1 - 1/γ²) = c√(1 - 1/4) = c√(3/4) = 0.866c

So the electron is moving at a velocity of 0.866 times the speed of light, which is approximately 0.94c. Therefore, the correct answer is E.

An Electron Is Accelerated from Rest Through a Potential Difference