A sample contains 10 - 2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2 . The ratio of the amounts of A and B after 16 s is x 100 . The value of x is _____ .

Step-by-step solution

Ratio of number of moles of substance in the beginning will be, N 0 A N 0 B = 10 - 2   kg M A 10 - 2   kg M B = M B M A = 1 2 . Number of half-life in 16   s for element A will be, n A = 16 4 = 4 Number of half-life in 16   s for element B will be, n B = 16 8 = 2 Hence, ratio of number of nuclei after 16   s will be, = N 0 A × 1 2 n A N 0 B × 1 2 n B = 1 2 × 1 2 4 - 2 = 1 8 = 25 100 Thus, value of x is 25 .