The activity of a radioactive material is 2.56 × 10⁻³ Ci. If the half life of the material is 5 days, after how many days the activity will become 2 × 10⁻⁵ Ci ?

Solution

Physics sir · 4 steps

Divide the starting activity by the final one, and see how many times you halved it to get there.

1. Halving rule. Every half-life the activity drops to half. After n half-lives it is A₀/2ⁿ.

   A₀/A = (2.56 × 10⁻³)/(2 × 10⁻⁵) = 128 = 2⁷

2. Count half-lives. Since 2ⁿ = 128, we get n = 7. The activity has halved seven times.
3. Convert to days. Each half-life is 5 days, so the time is 7 × 5 = 35 days.
4. So. The activity falls to 2 × 10⁻⁵ Ci after 35 days, option (b).

The idea to keep. When the ratio of activities comes out as a clean power of 2, skip logarithms. The power is the number of half-lives; multiply by the half-life to get the time.

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