A 232Th (thorium) nucleus at rest decays to a 228Ra (radium) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 × 10?13 J. An alpha particle has 1.76% of the mass of a 228Ra nucleus. Calculate the kinetic energy of (a) the recoiling 228Ra nucleus and (b) the alpha particle.

Solution 102P Step 1: Initially the 232Th nucleus was at rest and decays into a 228Ra nucleus and an alpha particle. By the conservation of momentum, m V = m V --------------------(1) Ra Ra But it is given that, m 0.0176 m Ra -----------------(2) By putting this value in equation (1), m Ra Ra = 0.0176 m Ra V V = 0.0176 V ----------------------(3) Ra