A radio active isotope has a half - life of 'T' years. How long will it take the activity to reduce to (a) `3.125% ` (b) `1%` of the original value.

Explanation

We know that, `t=(2.303)/(lambda) log (A_(0)/(A))`
`"i.e., " t=(2.303T)/(0.693) log (A_(0)/(A))`
`{:("i.e., "t=3.323T log ((A_(0))/(A))", ",(A)/(A_(0))=(3.125)/(100)=(3(1)/(8))/(100)),(" "t=3.323T log (32)",",(A)/(A_(0))=(cancel 25^(1))/(8xxcancel 100^(4))=(1)/(32)):}`
`therefore " "t=5.00T` years
Similarly, `t=3.323 T log ((100)/(1))=6.646T`
or `t=6.65T` years to reduce to `1%`