A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample is

Solution

Physics sir · 3 steps

Decayed 7/8 means only 1/8 is left, and 1/8 is three halvings: 15 minutes over 3 half-lives.

1. What remains. If 7/8 of the sample has decayed, the fraction still left is 1 - 7/8 = 1/8. The decay law always works with the amount remaining.

   N/N₀ = (1/2)ⁿ = 1/8 ⇒ n = 3

2. Count half-lives. Each half-life halves what is left: 1 → 1/2 → 1/4 → 1/8. So 3 half-lives fit into the 15 minutes.
3. So. T_(1/2) = (15 min)/3 = 5 min, which is option (a).

The idea to keep. Always convert the decayed fraction into the remaining fraction first. Then write it as (1/2)ⁿ, and the time divided by n is the half-life.

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