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

Explanation

`N_(0)=` Nuclei at time t = 0
`N_(1)=` Remaining nuclei after `40%` decay
`=(1-0.4)N_(0)=0.6N_(0)`
`N_(2)=` Remaining nuclei after `85%` decay
`=(1-0.85)N_(0)=0.15N_(0)`
`therefore" "(N_(2))/(N_(1))=(0.15N_(0))/(0.6N_(0))=(1)/(4)=((1)/(2))^(2)`
Hence, two half life is required between `40%` decay and `85%` decay of a radioactive substance.
`therefore" Time taken "=2tau_(1//2)=2xx"30 min "="60 min"`