I know that you\'d solve it using by applying the law of conservation of momentu

Question

I know that you'd solve it using by applying the law of conservation of momentum, but I'm not exactly sure how to set it up.

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 times10-27 kg and 234Th nucleus of mass 3.88 times 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 5.05 times10 m/s, what would be the recoil speed of the thorium nucleus? Answer in units of m/s

Explanation / Answer

Let the mass of Uranium parent be Mu
Of Thorium be Mt and Alpha be Ms

By law of conservation of komentum,

m1u1 +m2u2 = m1v1 = m2v2
where u representas initial and v final velocity

Here Mu* 0 = Mt*v1 + Ma*5.05*10^6

or -6.64*10^-27*5.05*10^6/3.88*10^-25= -8.6 + 10^4 m/s

Ans: velocity of Thrium nicleus is 8.6 * 10^4 m/s in opposite to alpha.

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