The half life of a radioactive substance is `5xx10^(3)`yrs. In how many years will its activity decay to 0.2 times its initial activity? Take `log_(10) 5=0.6990`.

Answer

`11615yrs`

Explanation

Here, `T=5xx10^(3) yr, t=?`
`A/(A_(0))=0.2=1/5 =(lambdaN)/(lambdaN_(0))=e^(-lambdat)`
`log_(e) 1 - log_(e) 5=-lambdat=-0.693/Tt`
`0-2.303xx0.6990=-0.693/(5xx10^(3))t`
`t=(2.303xx0.6990xx5xx10^(3))/0.693 yrs`
`=11615 yrs`