The half life of a radioactive substance is T. The time taken, for disintegrating 7/8th part of its original mass will be:

Solution

Physics sir · 3 steps

Do not count what decayed; count what is left. One-eighth remaining means three halvings.

1. What remains. If 7/8 of the mass has disintegrated, the part still left is 1 - 7/8 = 1/8 of the original.
2. Halve repeatedly. Each half-life cuts the remaining mass in half: 1 → 1/2 → 1/4 → 1/8. That is three halvings.

   N/N₀ = (1/2)ⁿ = 1/8 ⇒ n = 3

3. So. Three half-lives take t = 3T, which is option (b).

The idea to keep. Half-life questions are always about the fraction remaining. Write it as (1/2)ⁿ and n tells you how many half-lives have passed.

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