A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10 2 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S.
-Determine the total energy of particle A.

Question

Quizplus · Accepted Answer

First, we can use the formula for relativistic kinetic energy to find that each particle has kinetic energy of:

K = (gamma - 1) * m_0 * c^2

where gamma is the Lorentz factor, m_0 is the rest mass, and c is the speed of light. Plugging in the given values, we get:

K = (1 / sqrt(1 - v^2 / c^2) - 1) * 1.40 × 10^12 MeV

K = 1.059 × 10^12 MeV

Since the particles have equal and opposite momenta, their total energy is just twice this kinetic energy:

E = 2K

E = 2.118 × 10^12 MeV

We can convert this to MeV using the conversion factor 1.602 × 10^-13 J/MeV:

E = 338.8 MeV

Finally, since each particle has rest energy of 1.40 × 10^12 MeV, we can add this to the kinetic energy to find the total energy of particle A:

E_A = K + 1.40 × 10^12 MeV

E_A = 1.249 × 10^12 MeV

Again, converting to MeV:

E_A = 249 MeV

Therefore, the correct answer is D) 249 MeV.

A Subatomic Particle X Spontaneously Decays into Two Particles, a and B