A heavy parent nucleus initially at rest emits an α-particle. The daughter nucleus has mass number 206. Neglect the small difference between nuclear mass and mass number. What is the approximate ratio of α-particle kinetic energy to daughter-nucleus recoil kinetic energy?
Options

Question

A heavy parent nucleus initially at rest emits an α-particle. The daughter nucleus has mass number 206. Neglect the small difference between nuclear mass and mass number. What is the approximate ratio of α-particle kinetic energy to daughter-nucleus recoil kinetic energy?

Options

G1 Physics · Accepted Answer

The parent is initially at rest, so daughter and α-particle emerge with equal momentum magnitude p. For a non-relativistic particle, K = p² ÷ (2M). Therefore, for equal p, K is inversely proportional to M. Hence, K(α) : K(D) = M(D) : M(α) = 206 : 4 = 103 : 2. Correct option: B.