If the total energy of an electron in an accelerator is five times its rest energy, what is its speed? (c = 3.00 *10⁸ m/s) A) 1.98 * 10⁸ m/s B) 2.94 * 10⁸ m/s C) 2.32 * 10⁸ m/s D) 2.90 * 10⁸ m/s

Question

Quizplus · Accepted Answer

The total energy is given by E = γmc², where γ = 1/√(1-v²/c²). If E = 5mc², then γ = 5. Solving for v gives v = c√(1-1/γ²) = c√(1-1/25) = c√(24/25) ≈ 0.98c, which corresponds to 2.94 x 10^8 m/s.

If the Total Energy of an Electron in an Accelerator