Calculate the half life period of a radioactive substance if its activity drops to `1/16` th of its initial value in 30 years.

Explanation

Let `N_(0)` be the number of atoms present in the sample initially. We know that activity `propto` Number of atoms present. Number of atoms after 30 years is
`N= N_(0)/16`
Also, `N = N_(0) (1/2)^(n)`
where n is the number of half-lives.
`therefore N_(0)(1/2)^(n) = N_(0)/16`
`rArr (1/2)^(n) =(1/2)^(4)`
`rArr n=4`
Given, time of disintegration, t = 30 years
`therefore` Half-life is given by
`t_(1//2) =t/n = 30/4 = 7.5` years.