The disntergration rate of a certain radioactive sample at any instant is `4750 dp m`. Five minute later, the rate becomes `2700 dp m` Calculate half-line of sample.

Explanation

`r_(0) = 4750` dpm at `t = 0`
`r_(t) = 2700 dpm` at `t = 5` min.
`:. (r_(0))/(r_(t)) = (4750)/(2700)`
Also Rate `prop` NO. of atoms
`:. (r_(0))/(r_(t)) = (N_(o))/(N_(t)) = (4750)/(2700)`
`:. T = (2.303)/(lambda) log_(10) (N_(0))/(N_(t))`
`5 = (2.303)/(lambda) log_(10) (4750)/(2700)`
`lambda = 0.113 "mintute"^(-1)`
`:. t_(1//2) = (0.693)/(0.113) = 6.13` minute