The half life period of a radioactive substance is 60 days. The time taken for 7/8th of its original mass to disintegrate will be :

Solution

Physics sir · 3 steps

If 7/8 has decayed, only 1/8 is left. That is three halvings, so three half-lives.

1. Find what remains. The question gives the part that has disintegrated. The part still left is 1 - 7/8 = 1/8 of the original mass.

   N/N₀ = (1/2)ⁿ = 1/8 ⇒ n = 3

2. Count the halvings. Each half-life halves what is left: 1 → 1/2 → 1/4 → 1/8. That takes n = 3 half-lives.
3. So. Time = 3 × 60 = 180 days, which is option (c).

The idea to keep. Always turn the fraction decayed into the fraction remaining first. Then write that remaining fraction as (1/2)ⁿ, and the time is n half-lives.

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