In α decay the kinetic energy of α particle is 48 MeV and Q value of the reaction is 50 MeV . The mass number of the mother nucleus is (Assume that the daughter nucleus is in the ground state)

Step-by-step solution

Let K α is kinetic energy of α particle and K d is the kinetic energy of the daughter nucleus. Let A be the mass number of mother nucleus then the mass number of the daughter nucleus is A - 4 . From the conservation of momentum K α K d = p 2 2 4 2 A - 4 p 2 K α K d = A - 4 4 K d = 4 A - 4 K α Q value = K α + K d 50 = 48 + 4 A - 4 48 2 = 4 A - 4 48 A - 4 = 96 A = 100