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

Key Concept After n half-life, the numberof nuclei left undecayed is given as
`N= N_(0)(1/2)^(n)` where, `n=t/t_(1//2)`
Here, initially numberof nuclei, `N_(0) = 600`
After disintegration, number of nuclei, `N^(') = 450`
`therefore` Number of nuclei left undecayed
`N=N_(0) -N^(') = 600-450=150`
Half-life, `t_(1/2) = 10 min`
As, `N/N_(0) = (1/2)^t//10`
or `(1/2)^(2) = (1/2)^(t//10)` or `t/10 = 2`
rArr t= 20 min