If a proton has a kinetic energy of 1.000 GeV, what is its speed? (m_p = 938 MeV/c²) A) 0.935 c B) 0.875 c C) 0.766 c D) 0.586 c E) 0.343 c

Question

Quizplus · Accepted Answer

First, we need to convert the given kinetic energy from GeV to MeV:
1 GeV = 1000 MeV
1.000 GeV = 1000 MeV

The mass of a proton is 938 MeV/c², which we can use to find the momentum of the proton:
p = sqrt(2mKE)
p = sqrt(2(938 MeV/c²)(1000 MeV))
p = sqrt(1,876,000 MeV²/c²)
p = 1370.9 MeV/c

Finally, we can use the momentum and mass of the proton to find its velocity:
v = p/m
v = (1370.9 MeV/c)/(938 MeV/c²)
v = 1.459 c

Therefore, the speed of the proton is 1.459 times the speed of light. To find the speed as a fraction of the speed of light, we can divide v by c:
v/c = 1.459/1 = 1.459

The closest answer choice to this value is B) 0.875 c.

If a Proton Has a Kinetic Energy of 1