The half lives of two radioactive nuclides A and B are 1 and 2 min. respectively . Equal weights of A and B are taken separately and allowed to disintegrate for 4 min. What will be the ratio of weigths of A and B disintegrated ?

Options

A. `1 : 1`
B. `5 : 4`
C. `1 : 2`
D. `1 : 3`

Answer

B

Explanation

`{:("For A","For B"),(T = 4 min,T = 4 min),(t_(1//2) = 1min,t_(1//2) = 2 min),(N_(0) = x("say"),N_(0)= x("say")),(n = 4//1 = 4,n = 4//2 = 2),(N = (N_(0))/(2^(n)) = (x)/(2^(4)),N = (N_(0))/(2^(n)) = (x)/(2^(2))),(N = (x)/(16),N = (x)/(4)),("A disintegrated","B disintegrated"),(x - (x)/(16) = (15)/(16)x,x - (x)/(4) = (3x)/(4)),("Ratio of A B disintegrated",),((15)/(16)x : (3x)/(4) rArr 5 :4,):}`