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

charge , q=It = `10^(-4)xx1xx3600 = 0.36C`
number of protons ` =(q)/( E) =(0.36)/(1.6xx10^(-19))=2.25xx10^(18)`
number of `""^(7)Be` nuclei `=(2.25x10^(18))/(1000)=2.25xx10^(15)`
Activity ,R `=("in 2)/(T_(1//2))N,` where ` R= 2.8xx10^(8)` dps (given )
half - life of substance , `T_(1//2)=("N in"2)/(R) =(2.25xx10^(15)xx0.693)/(2.8xx10^(8))`
`=0.556xx10^(7)s`