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

Answer:

4.999 × 10⁴ MeV

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 = $1/\sqrt{1-v^2/c^2}$

So γ =  $1/\sqrt{1- (0.99217 c)^2/c^2}$= 8.0067

⇒ K = (8.0067-1)(7134) = 49986 MeV

                                       =49,999 MeV ( 4 significant figures)