a uranium-238 nucleus may stay in one piece for billions of years, but later it decays into an a particle of mass 6.64 x 10^-27 and a thorium-234 nucleus of mass 3.88 x 10^-25. The decay process itself is extremely fast (about 10^-20 s).

Question

a uranium-238 nucleus may stay in one piece for billions of years, but later it decays into an a particle of mass 6.64 x 10^-27 and a thorium-234 nucleus of mass 3.88 x 10^-25.  The decay process itself is extremely fast (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 1.4 x 10^7 m/s, what would be the recoil speed of the thorium nucleus?

Please help.  I don't know where to begin.

bobpursley · Answer

Use the law of conservation of mometum. the total momentum of the two particles before the ejection was zero... 0=mass234*Vth+ massalpha*Valpha solve for Valpha