Question

An atomic nucleus with a rest mass energy of 7134 MeV is accelerated to 99.217% the speed of light relative to the lab frame. What is the Kinetic Energy in MeV of the atomic nucleus in the lab frame? Assume 4 significant figures.

Answer 1

4.999 × 10⁴ MeV

Step-by-step explanation:

Kinetic energy is related to the rest energy by the Lorentz transformation equation as shown below.

Kinetic energy in the lab frame K= ( γ -1 ) Eo

The Lorentz constant γ =
`1/√(1-v^2/c^2)`

So γ =
`1/√(1- (0.99217 c)^2/c^2)`= 8.0067

⇒ K = (8.0067-1)(7134) = 49986 MeV

=49,999 MeV ( 4 significant figures)