Question

At rest, a uranium atom U238 decays into an alpha particle and a thorium atom Th234. Radioactive decay is like an elastic collision run backward; the particles begin stuck together and end by flying apart. In this process 8.64x10-13 J of energy is liberated. The mass of an alpha particle is 6.68x10-27 kg, and the mass of thorium is 3.91x10-25 kg. What is the momentum of the alpha particle after the decay?

Answer 1

$$Mu-mv=0\\ p=mv=Mu$$

$$E=0.5Mu^2+0.5mu^2=\frac{p^2}{2M}+\frac{p^2}{2m}$$

$$(8.64\cdot10^{-13})=\frac{p^2}{2(3.91\cdot10^{-25})}+\frac{p^2}{2(6.68\cdot10^{-27})}$$

$$p=1.07\cdot10^{-19}\frac{kg\cdot m}{s}$$