Question

The half-life of iodine-131 is 7.2 days. How long will it take for a sample of this substance to decay to 30% of its original amount?

Answer 1

To decay `30%` of original amount it will take `12.51` days.

Explanation:

Half life of iodine -131 is `t=7.2` days

We know `p(t)=p(0)*e^(kt) or e^(kt) = (p(t))/(p(0))= 1/2=0.5`

Taking natural log on both sides we get,

`kt= ln(0.5) or 7.2k = ln(0.5) or k=ln(0.5)/7.2 ~~-0.09627`

When `(p(t_0.3))/(p(0))=0.3 :. e^(kt_0.3) = (p(t_0.3))/(p(0))=0.3` or

`k*t_0.3= ln(0.3):. 0.09627*t_0.3=ln(0.3)` or

`t_0.3=ln(0.3)/-0.09627~~12.51(2dp)` days

To decay `30%` of original amount it will take `12.51`days. [Ans]