If the kinetic energy of a particle is 3.00 times its rest energy,the speed of the particle is closest to which of the following values?
A)0.950c
B)0.968c
C)0.976c
D)0.984c
E)0.990c

Question

Quizplus · Accepted Answer

According to the equation E^2 = (pc)^2 + (mc^2)^2, where E is the total energy, p is the momentum, m is the rest mass, and c is the speed of light, we have E = mc^2 + K, where K is the kinetic energy. Given K = 3mc^2, we have E = 4mc^2. Equating this to the relativistic energy-momentum equation E^2 = (mc^2)^2 + (pc)^2, we get (pc)^2 = 3(mc^2)^2. Therefore, p = (√3)mc. The velocity of the particle is given by v = p / (√(p^2 + m^2c^2)). Substituting p and m, we get v = (√3)c / 2, which is closest to 0.968c. Therefore, the best choice is B.

If the Kinetic Energy of a Particle Is 3