A `.^7Li` target is bombarded with a proton beam current of `10^-4` A for `1` hour to produce `.^7 Be` of activity `1.8xx10^8` disintegrations per second.
Assuming that `.^7Be` radioactive nucleus is produced by bombarding `1000` protons, determine its half-life.

Explanation

`q =it = 10^(-4)xx1xx3600 = 0.3 C`
Number of protons `= (q)/(e) = (0.36)/(1.6xx10^(-19)) = 2.25xx10^(18)`
Number of `.^(7)Be` nuclei `= (2.25 xx 10^(18))/(1000) = 2.25 xx 10^(15)`
`A = 1.8 xx 10^(8) dps`
`= lambdaN = (ln2)/(T_(1//2))N`
`T_(1//2) = (Nln2)/(A) = (2.25xx10^(15)xx0.693)/(1.8xx10^(8))`
`= 0.87 xx 10^(7)sec`