A mixture consists of two radioactive materials A₁ and A₂ with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A ₁ and 160 g of A ₂ . The amount of the two in the mixture will become equal after

Step-by-step solution

For radioactive material A ₁ , N ₁= N _ ol ( 1 2 )^ n =40 ( 1 2 )^ t _ 1 / 20 (i) For radioactive material N ₂= N _ o 2 ( 1 2 )^ n ₂ =160 ( 1 2 )^ t ₂ / 10 (ii) As, N₁=N₂ 40 ( 1 2 )^ t₁ / 20 =160 ( 1 2 )^ t₂ / 10 1 4 = ( 1 2 )^ t 10 - t 20 = ( 1 2 )^ t 20 aligned & ( 1 2 )^2= ( 1 2 )^ t 20 & t 20 =2 t =40 ~s aligned