The disintegration rate of a certain radioactive sample at any instant is `4750` disintegrations per minute. Five minutes later the rate becomes `2700` per minute. Calculate
(a) decay constant and (b) half-life of the 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