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`.

Explanation

`T= 5000` years,
`(N)/(N_(0))=0.2=(2)/(10)=(1)/(5)`
`lambda=(0.693)/(T)=(0.693)/(5000)`
`(N)/(N_(0))=e^(-lambdat)`
`(1)/(5)=(1)/(e^(lambdat))rArr5=e^(lambdat)`
`log_(e )^(5)=lambdat`
`t=(2.303xx0.6990xx5000)/(0.693)`
`t=11614.6` years `=1.1615xx10^(4)` years