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 1.07×10^7 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 1.07×10^7 m/s, what would be the recoil speed of the thorium nucleus? 
Answer in units of m/s.

I got -183113.4021m/s, but that was wrong, and so was 183113.4021m/s

drwls · Answer

Don't use so many significant figures. I get 1.83*10^5 m/s