In a radioactive substance at `t = 0`, the number of atoms is `8 xx 10^4`. Its half-life period is `3` years. The number of atoms `1 xx 10^4` will remain after interval.

Options

A. 9 years
B. 8 years
C. 6 years
D. 24 years

Answer

A

Explanation

(a) By formula `N = N_0((1)/(2))^(t//T)`
or `10^4 = 8 xx 10^4 ((1)/(2))^(t//3)`
or `((1)/(8)) = ((1)/(2))^(t//3)` or `((1)/(2))^3 = ((1)/(2))^(t//3) rArr 3 = (t)/(3)`
Hence `t = 9 years`.