An unstable particle of mass M decays into two identical particles, each of mass m. Obtain an expression for the velocities of the two decay particles in the labframe. (a) if M is at rest in the lab and (b) if M has total energy 4mc2 when it decays and the decay particles move along the direction of M.

A deuteron, consisting of a proton and neutron and having mass 3.34 x 10-27 kg, is traveling at 0.950c relative the Earth in a linear accelerator. Calculate the deuteron's rest energy, y-factor, total energy, and kinetic energy. (a) rest energy (Give your answer to at least three significant figures.) (b) y-factor (c) total energy (d) kinetic energy

A kaon with a speed 0.8c in the laboratory decays into two pions, one positively charged and the other negatively charged. The rest mass of the kaon is 498 MeV/c2 and the rest mass of the pion is 140 MeV/c2. (a) What is the total energy of the kaon in the laboratory frame? (b) In the rest frame the two pions must go off in opposite directions to conserve momentum. What is the energy of each of the pions in the kaon rest frame? (c) Assume that the positive pion continues to travel in the same direction as the kaon was traveling. What is the total energy of each of the pions in the laboratory? (d) In what direction, relative to the kaon’s original direction of travel, does the negatively charged pion travel?

A particle is created in a lab. Its kinetic energy is equal to its mass energy. If the particle travels a distance d before it decays, find an expression that shows how long the particle lived in its own rest frame.