Question

The (radio) activities, of two materials X and Y, when they are having N₁ and N₂ atoms, are R₁ and R₂ , respectively. It is observed that R₂ = 3R₁ , when N₁ = 2N₂ . If the half life of X is 1 month, that of Y would be

(1) 6 months

(2) 3 months

(3) 1/3 months

(4) 1/6 months

Answer 1

(4) 1/6 months

Let λ₁ and λ₂ and be the disintegration constants of X and Y. N₁ and N₂ are their number of atoms, at the given instant. Then

Let \(\tau_1\) and \(\tau_2\) be the half–life of X and Y, respectively. We know that half–life is inversly proportional to the disintegration constant. Therefore