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) half -life of a radioactive substance is ,
`T_(1//2)prop log ((N_(0))/(N))`
given , `N_(1) =0.6N_(0) ( :' 40%" decay")`
`N_(2) =0.5 N_(0) ( :' 85% "decay")`
Putting these in the formula ,
`((N_(2))/(N_(1)))=(0.15N_(0))/(0.6 N_(0) )=(1)/(4)=((1)/(2))^(2)`
so two half life periods has passed .
thus , time taken `=2xxt_(1//2)=2xx30=60 `min