A nucleus of mass M+Δm at rest decays into two daughter nuclei of masses M/4 and 3M/4. Find the speed of the daughter of mass M/4, assuming non-relativistic motion.
Options

Question

A nucleus of mass M+Δm at rest decays into two daughter nuclei of masses M/4 and 3M/4. Find the speed of the daughter of mass M/4, assuming non-relativistic motion.

G1 Physics · Accepted Answer

The released energy is Δmc². Equal daughter momenta give K₁/K₂=m₂/m₁=3, so the M/4 daughter gets 3Δmc²/4. Thus ½(M/4)v²=3Δmc²/4, giving v=c√(6Δm/M). Correct answer: D.