Question

A uranium nucleus 238U may stay in one piece for billions of years, but sooner or later it decays into an α particle of mass 6.64 x 10^−27 kg and 234Th nucleus of mass 3.88 x 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.
a) If the α particle is emitted at a speed of 5.24 x 10^6 m/s, what would be the recoil speed of the thorium nucleus?
Answer in units of m/s

Answer 1

Answer: The recoil speed is - 8.9604.$10^{4}$ m/s.

Explanation: According to the Third Law of Newton, every action has an oppsite and equal reaction, and the Second Law of Newton, Force=mass·acceleration. Acceleration is a variation in velocity by any given time, so Force = mass·velocity·time.

Combining the two laws, there is : m1·v1 = - m2·v2. This is the Law of Conservation of Momentum.

Substituting and calculating:

v2 = - ($\frac{m1}{m2}$) · v1

v2 = - $\frac{6.64.10^{-27} }{3.88.10^{-25} }$ · 5.24.$10^{6}$

v2 = - 8.9604.$10^{4}$

The recoil speed of the thorium nucleus is - 8.9604.$10^{4}$m/s.