Question

A uranium 238 nucleus, initially at rest emits an alpha particle with a speed of `1.4xx10^7m/s`. Calculate the recoil speed of the residual nucleus thorium 234. Assume that the mas of a nucleus is proportional to the mass number.

Answer 1

Applying principle of conservation of linear momentum
`m_(alpha)upsilon_(alpha)+m_(r)upsilon_(r)0 :. upsilon_(r)=-(m_(alpha))/(m_(r))xxupsilon_(alpha)`
When `_(2)He^(4)` is emitted from `U^(238)`, residual nucleus has a mass `m_(r)=238-4=234`
`:. upsilon_(r)=-(4)/(234)xx1.4xx10^(7)m//s=-2.4xx10^(5)m//s`