Initially at rest, a uranium-238 nucleus emits an alpha particle with a speed of 1.4 imes 10^7 m/s . Determine the recoil speed of the residual thorium-234 nucleus. Assume that the mass of a nucleus is proportional to its mass number.

Step-by-step solution

By the law of conservation of linear momentum, the initial momentum of the system is zero. Therefore, the magnitude of the momentum of the residual thorium nucleus is equal to the magnitude of the momentum of the alpha particle. m_ Th v_ Th = m_ v_ Given that the mass of a nucleus is proportional to its mass number, m_ Th 234 and m_ 4 . 234 v_ Th = 4 1.4 10^7 v_ Th = 4 1.4 10^7 234 v_ Th = 5.6 10^7 234 v_ Th 2.39 10^5 m/s 2.4 10^5 m/s