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

Correct option : (4) 1/6 months

Explanation : 

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 τ₁ and τ₂ be the half–life of X and Y, respectively. We know that half–life is inversely proportional to the disintegration constant. Therefore