The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:
A) mc/2
C) mc
E) 2mc

Question

The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:
A) mc/2 
C) mc 
E) 2mc

Quizplus · Accepted Answer

The total energy of a particle is given by E = γmc^2, where γ is the Lorentz factor, which is given by γ = 1/√(1-(v/c)^2). If the total energy is twice the rest energy (E = 2mc^2), then γ = 2. Solving for v/c, we get v/c = √(1-1/γ^2) = √(3/4) = √(12/16) = √(12)/4. Therefore, the momentum of the particle is p = γmv = m/(√(1-(v/c)^2)) * v = m/(√(1-3/4)) * √(12)/4 = m/(√(1/4)) * √(12)/4 = 2mc/√3 = (2/√3) mc. Simplifying the expression, we get p ≈ 11eaafba_aeff_3571_a7a5_ef7f3d20b22c_TB3976_11.

The Mass of a Particle Is M