Question

The yeild of a nuclear reaction producing radionuclides may be described in two ways: either by the ratio `omega` of the numbers of nuclear reactions to the number of bombarding particles, or by the quantity `k`, the ratio of the activity of the formed radionuclide to the number of bombarding particles, Find:
(a) the half-life of the formed radionuclide, assuming `omega` and `k` to be known:
(b) the yield `omega` of the reaction `Li^(7)(p,n)Be^(7)` if after irradiation of a lithum target by a beam or protons(over `t=2.0`) hours and with `=1.35.10^(8)dis//s` and its half-life to `T=53 days`.

Answer 1

(a) Assuming of course, that each reaction produces a radio nuclide of the same type, the decay constant `alpha` of the radionuclide is `k//w`. Hence `T=(In 2)/(lambda)=(w)/(l)In2`
(b) number of bombarding particles is : `(It)/(e )`
(e = charge on proton.) Then the number of `Be^(7)` produced is : `(It)/( e)w`.
If `lambda=` decay constant of `Be^(7)=(In2)/(T)`, then the acitvity is `A=(It)/(e )omega. (In2)/(T)`
Hence `w=(eAT)/(It In 2)= 1.98xx10^(-3)`