A nuclear reaction occurs when an incident projectile strikes a stationary target nucleus. The sum of the rest masses of the resulting products is found to be 3.0 MeV /c^2 greater than the sum of the rest masses of the initial reactants. If the incident projectile has a kinetic energy of 5.5 MeV , what is the total kinetic energy of the products?

Step-by-step solution

The Q -value of a nuclear reaction is defined as the energy equivalent of the mass difference between reactants and products: Q = (m_ reactants - m_ products )c^2 We are given that the mass of the products is 3.0 MeV /c^2 greater than the mass of the reactants. Therefore, the mass defect is negative: Q = -3.0 MeV By the principle of conservation of total energy, the total kinetic energy of the products ( K_ prod ) is the sum of the initial kinetic energy of the projectile ( K_p ) and the Q -value: K_ prod = K_p + Q