A uranium nucleus 238U may stay in one piece for billions of years, but sooner or later it decays into an a particle of mass 6.64×10−27 kg and 234Th nucleus of mass 3.88 × 10−25 kg, and the decay process itself is extremely fast(it takes about 10−20 s). Suppose the uranium nucleus was at rest just before the decay. If the a particle is emitted at a speed of 1.07×107 m/s, what would be the recoil speed of the thorium nucleus?

Question

A uranium nucleus 238U may stay in one piece for billions of years, but sooner or later it decays into an a particle of mass 6.64×10−27 kg and 234Th nucleus of mass 3.88 × 10−25 kg, and the decay process itself is extremely fast(it takes about 10−20 s). Suppose the uranium nucleus was at rest just before the decay. If the a particle is emitted at a speed of 1.07×107 m/s, what would be the recoil speed of the thorium nucleus?
Answer in units of m/s.

drwls · Answer

Conservation of momentum requires that: (alpha particle mass)x(alpha particle speed) = (Th234 speed)x (Th234 mass) The speeds are in opposite directions Therefore (Th34 speed)= (alpha speed)*(4/234)