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 a proton's kinetic energy equals its rest energy, its total energy is twice its rest energy. According to the theory of relativity, the relationship between total energy (E), rest energy (E_0), and kinetic energy (K) can be expressed as E = E_0 + K. If K = E_0, then E = 2E_0. The speed of the proton can be found using the formula for total energy: $E = \gamma E_0$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. Solving for $v$ when $E = 2E_0$ leads to $\gamma = 2$, which corresponds to $v \approx 0.87c$.

In a Certain Particle Accelerator,a Proton Has a Kinetic Energy