The disintegrationn rate of a certain radioactive sample at any instant is 4750 dpm which becomes 2700 dpm 5 min later. Calculate the half life to sample?

Explanation

`r_(0) = 4750 dmp` at `t = 0`
`r_(1) = 2700 dpm` at `t = 5` min
`:. (r_(0))/(r_(l)) = (4750)/(2700)`
Also rate nubmer `prop` number of atoms
`:. (r_(0))/(r_(l)) = (N_(0))/(N_(t)) = (4750)/(2700)`
`:.t = (2.303)/(K) "log" (N_(0))/(N_(t))`
`5 = (2.303)/(K) "log" (4750)/(2700)` or `K = 0.113 "min"^(-1)`
`:. t_(1//2) = (0.693)/(0.113) = 6.13` min