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. 20
B. 10
C. 30
D. 15

Answer

A

Explanation

`N_(0)= 600, N.= 450`
`N= N_(0)- N.`
N= 150
`(N)/(N_(0)) = ((1)/(2))^(t//T_(H)) rArr (150)/(600) = ((1)/(2))^(t//10)`
`rArr (1)/(4) = ((1)/(2))^(t//10) rArr ((1)/(2))^(2)= ((1)/(2))^(t//10)`
`2 = (t)/(10) rArr t=20` min