The half life of radon is 3.8 days . After how many days will only one twentieth of radon sample be left over ?

Explanation

We know that, `lambda = (0.693)/(t_(1//2)) = (0.693)/(3.8) = 0.182 "days"^(-1)`
Let the initial amount of radon be `N_(0)` and the amount left after t days be N which is equal to `(N_(0))/(20)`
Apply the equation,
`t = (2.303)/(lambda) log_(10) (N_(0))/(N)`
`= (2.303)/(0.182) log_(10) (N_(0))/(N_(0)//20) = (2.303)/(0.182) log_(10) 20`
= 16.54 days