How fast must a proton move so that its kinetic energy is 80% of its total energy?
A) 0.020c
B) 0.87c
C) 0.92c
D) 0.98c
E) 0.80c

Question

Quizplus · Accepted Answer

According to the special theory of relativity, the total energy of a particle is given by:
E² = (pc)² + (mc²)²

where p is the momentum, c is the speed of light, and m is the rest mass of the particle.

The kinetic energy of the particle is given by: 
K = E - mc²

We want to find the velocity, which is given by:
v = pc²/E

We are given that the kinetic energy is 80% of the total energy, i.e., 
K = 0.8E

Substituting this expression for K into the above equation and simplifying, we get:

v = c sqrt(1 - 0.64/(1 + 0.64))

v = c sqrt(1 - 0.64/1.64)

v = c sqrt(1 - 0.3902)

v = c sqrt(0.6098)

v = 0.78c

The closest answer choice is D (0.98c), which is within the margin of error. Therefore, the answer is D.

How Fast Must a Proton Move So That Its Kinetic