Kinetic energy: In a certain particle accelerator, a proton has a kinetic energy that is equal to its rest energy. What is the speed of the proton relative to the accelerator?
A) 0.25c
B) 0.50c
C) 0.71c
D) 0.75c
E) 0.87c

Question

Quizplus · Accepted Answer

When the kinetic energy (K) of a particle equals its rest energy (E₀), the total energy (E) is given by E = E₀ + K = 2E₀. According to the theory of relativity, the total energy E is related to the rest mass m₀ and the speed v by the equation E = γm₀c², where γ = 1/√(1 - v²/c²) and c is the speed of light. Setting E = 2E₀ implies γ = 2, which leads to 1/√(1 - v²/c²) = 2. Solving for v/c gives v/c = √3/2, which is approximately 0.87. Therefore, the speed of the proton relative to the accelerator is approximately 0.87c.

Kinetic Energy: in a Certain Particle Accelerator, a Proton Has