Half-life of a radioactive substance` A` and `B` are, respectively, `20 min` and `40min`. Initially, the samples of `A` and `B` have equal number of nuclei. After `80 min`, the ratio of the remaining number of `A` and `B` nuclei is

Options

A. `1 : 16`
B. `4 : 1`
C. `1 : 4`
D. `1 : 1`

Answer

C

Explanation

( c) For `80` minutes, number of half-lives of sample
`A = n_A = (80)/(20) = 4` and number of half-lives of sample
`B = n_B = (80)/(40) = 2`. Also by using `N = N_0((1)/(2))^n`
`rArr N prop (1)/(2^n) rArr (N_A)/(N_B) = (2^(nB))/(2^(nA)) = (2^2)/(2^4) = (1)/(4)`.