Two radioactive substances X and Y originally have N₁ and N₂ nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio N₁/N₂ will be equal to :

Solution

Physics sir · 3 steps

In the same time, X goes through twice as many half-lives as Y, so X must start with more nuclei.

1. Count half-lives. Let the half-life of Y be 2T, so the half-life of X is T. Three half-lives of Y take t = 6T. In that time Y completes 3 half-lives and X completes 6T/T = 6 half-lives.
2. Nuclei left. After n half-lives the number left is N₀/2ⁿ. So X has N₁/2⁶ = N₁/64 left, and Y has N₂/2³ = N₂/8 left.

   N₁/64 = N₂/8 ⇒ N₁/N₂ = 64/8 = 8

3. So. N₁ : N₂ = 8 : 1, which is option (d).

The idea to keep. When two samples decay for the same time, convert that time into the number of half-lives for each one. Then use N = N₀/2ⁿ separately for each sample.

Answer from the NTA final answer key. Solution by PrepWiser.