Question

Using the tabular values of atomic masses, find the threshold kinetic energy of an alpha paricles required to acitivate the nuclear reaction `Li^(7)(alpha, n)B^(10)`. What is the velocity of the `B^(10)` nucleus in this case?

Answer 1

The `Q of Li^(7) (alpha,n)B^(10)` was calculated in problem 266(c ). It is `Q= 2.79MeV`
Then the threshold energy of `alpha`-particle is
`T_(th)=(1+(m_(alpha))/(m_Li))|Q|=(1+(4)/(7))2.79= 4.38MeV`
The velocity of `B^(10)` in this case is simply the velocity of centre of mass:-
`v=sqrt(2m_(alpha)T_(th))/(m_(alpha)+m_(Li))=(1)/(1+(m_(Li))/(m_(alpha)))sqrt((2T_(th))/(m_(alpha)))`
This is beacuse both `B^(10)` and `n` are at rest in the `CM` frame at theshold. Substituting the values of various quantities
We get `v= 5.27cc10^(6)m//s`