Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be -

(A) `1 : 16`
(B) `4 : 1`
(C) `1 : 4`
(D) `5 : 4`

Options

A. `1:16`
B. `4:1`
C. `1:4`
D. `5:4`

Answer

D

Explanation

80 minutes = 4 half-lives of A = 2 half lives of B
let the initial number of nuclei in each sample be N.
Number of undecayed nuclides of element A after 80 minutes =`N/2^4`
`therefore` Number of A nuclides decayed =`15/16N`
Number of undecayed nuclides of element B after 80 minutes = `N/2^2`
`therefore` Number of B nuclides decayed =`3/4N`
Required ratio `=(15//16)/(3//4)=5/4`