The half-life of a radioactive substance is `30` minutes, The time (in minutes) taken between `40 %` decay and `85 %` decay of the same radioactive substance is.

Options

A. 15
B. 30
C. 45
D. 60

Answer

D

Explanation

`D.P_(1)=40%impliesA.P_(1)60%impliest_(1)`
`D.P_(2)=35%T_(1//2)log_(10)((1)/(A.P_(1)))`
`t_(2)=3.32T_(1//2)log_(10)((1)/(A.P_(2)))`
`t_(2)-t_(1)=3.32T_(1//2)[log_(10)((A.P_(1))/(A.P_(2)))]`
`=3.32xx30[log_(10)((60//100)/(15//100))]`
`=3.32xx30log_(10)4`
`=3.32xx30xx2log_(10)2`
`=59.95`
=60