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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? |
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Answer» Solution :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` |
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