Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

Solution

Physics sir · 4 steps

Do not look at what has decayed; look at what is left. 67% left falling to 33% left is one halving.

1. Switch to remaining. After 33% decay, 67% of the nuclei remain. After 67% decay, 33% remain. The decay law is written for the amount remaining, so use these.

   N₁/N₂ = (0.67 N₀)/(0.33 N₀) ≈ 2

2. One halving. The remaining amount drops to about half. Halving always takes one half-life, whatever amount you start from.
3. Exact check. t = T_(1/2)/(ln 2)ln 67/33 = 20/0.693 × 0.708 ≈ 20.4 minutes, which is 20 minutes to the nearest option.
4. So. The interval is one half-life, 20 minutes, which is option (d).

The idea to keep. Convert "percent decayed" into "percent remaining" first. If the remaining amount halves, exactly one half-life has passed, no matter where you start.

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