A radioactive sample has a half life of 30 minute. How long will it take for `(5)/(6)th` of the sample to disintegrate?

Explanation

`T_(1)/(2)=30` minutes. Initial number of atoms=No. the number of atoms which disintegrates in t minute=`((5)/(6))N_(0)`
`therefore` The number of atoms left after t minutes
`N=[1-(5)/(6)]N_(0)=(1)/(6)N_(0) ` But `N=N_(0)e^(lambdat)`
using `t=((2.303)/(lambda))(log.(N_(0))/(N))` We write
`t=(2.303)/(0.693)xx30 log (6)=99.697xx0.7782=77.58` minute.