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

Options

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

Answer

C

Explanation

`T_(1//2)=10` minutes
`N_(0)=600`
`N=600-450=150`
Let n half-lives are elapsed then
`N/N_(0)=(1/2)^(n)`
`150/600 = (1/2)^(n)`
`(1/2)^(n) =(1/2)^(n) rArr n=2`
Total time, `t=nT_(1//2)=2 xx 10 =20` minutes.