Question

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

Answer 1

Correct Answer - B
For `A_(1//2) = 20 min , t = 80 min , number of half life n = 4 `
`:. Nuclei remaining `(N_(0))/(2^(4)) ` Therefore nuclie decayed
`= N_(0) -(N_(0))/(2^(4))` for `B_(1//2) = 40 min , t = 80` min number of half life `n = 2`
:. Nuclei remaining ` = (N_(0))/(2^(2))` Therefore nuclei decayed
`= N_(0) = -(N_(0))/(2^(2))`
`:. Required ratio = (No- (No)/(2^(4)))/(No - (No)/(2^(2))) = (1- (1)/(16))/(1 - (1)/(2^(4 = )) = (15)/(16) xx (4)/(3) = (3)/(4)`