For a radioactive material, half-life is `10` minutes. If initially there are `600` number of nuclei, the time taken for the disintegratiom of `450` nuclei is.

Options

A. 20
B. 10
C. 30
D. 15

Explanation

Number of nuclei remaining
`N=600-450=150`
According to the law of radioactive decay,
`(N)/(N_(0))=((1)/(2))^((t)/(T_(1//2)))`, where `N_(0)` is the number of nuclei initially.
`therefore" "(150)/(600)=((1)/(2))^((t)/(T_(1//2)))`, where `T_(1//2)=` half life.
`"or "((1)/(2))^(2)=((1)/(2))^((t)/(T_(1//2)))rArr t=2T_(1//2)=2xx"10 minutes"`
= 20 minutes