The initial amount of 2 radioactive elements X and Y is 1 g each and their half-lives are 12 hours and 16 hours respectively. The ratio of X and Y after 2 days is:

Step-by-step solution

The amount of a radioactive substance remaining after time t is given by N(t) = N₀ ( 1 2 )^ t/T_ 1/2 , where N₀ is the initial amount and T_ 1/2 is the half-life. Given t = 2 days = 48 hours. For element X: N₀ = 1 g, T_ 1/2 = 12 hours. The number of half-lives is n_X = 48 12 = 4 . N_X = 1 ( 1 2 )⁴ = 1 16 g. For element Y: N₀ = 1 g, T_ 1/2 = 16 hours. The number of half-lives is n_Y = 48 16 = 3 . N_Y = 1 ( 1 2 )³ = 1 8 g. The ratio of X to Y after 2 days is N_X N_Y = 1/16 1/8 = 8 16 = 1 2 . Answer: 1:2