In an α-decay, the α-particle kinetic energy is 48 MeV and the Q-value is 50 MeV. Assuming the daughter is in the ground state, find the mass number of the mother nucleus.
Physics · Nuclear physics
JEE Mains Advanced

Question

In an α-decay, the α-particle kinetic energy is 48 MeV and the Q-value is 50 MeV. Assuming the daughter is in the ground state, find the mass number of the mother nucleus.

G1 Physics · Accepted Answer

In two-body α-decay, daughter and α have equal momenta, so Kα/Kd = Md/Mα ≈ (A−4)/4. With Kα=48 MeV and total Q=50 MeV, Kd=2 MeV. Thus 48/2=(A−4)/4, giving A=100.