Question

If a particle at rest decays into 2 lighter particles one of mass 1 MeVc^-2 traveling at 80 percent of the speed of light and the other at 2 MeVc^-2. Show that the original particle has a mass of 4.7 MeVc^-2.

Answer 1

Solution ;

Energy of a particle is given as E = where P is the momentum of the particle c is Velocity of light , M is mass of the particle . let E₁ and E₂ be the Energy of the first and second particle , E is the energy of initial particle before decay. so Conservation of Energy we have

           total energy before decay = total energy after decay

                         E = E₁ + E₂   

first particle has a mass 1Mev/c² and velocity = 0.8C and second particle has rest mass 2Mev

so momentum of first particle , which implies

so

so and we have rest mass energy of second particle

so E = 2.778+2 = 4.778 MeV