A proton with mass 1.67 x 10^-27 kg moves in an accelerator with a speed of 0.800 c.What is its total energy? (c = 3.00 x 10⁸ m/s) A)0.540 x 10^-10 J B)1.08 x 10^-10 J C)2.51 x 10^-10 J D)3.26 x 10^-10J

Question

Quizplus · Accepted Answer

Using the formula for total energy of a particle, E = γmc², where γ is the Lorentz factor and m is the mass of the particle:
γ = 1/√(1-(v/c)²)   (where v is the velocity of the proton)
γ = 1/√(1-(0.8c/c)²) = 1/√(1-0.64) = 1/0.7682 = 1.302
E = γmc² = (1.302)(1.67 x 10^-27 kg) (3.00 x 10^8 m/s)^2 = 2.51 x 10^-10 J
Therefore, the correct answer is (C).

A Proton with Mass 1