The activity of a radioactive material is 6.4 × 10⁻⁴ curie. Its half life is 5 days. The activity will become 5 × 10⁻⁶ curie after :

Solution

Physics sir · 3 steps

Find how many times the activity halves, then multiply that count by the half-life.

1. Activity halves too. Activity A = λ N is proportional to the number of undecayed nuclei. So every half-life the activity also drops to half.

   A₀/A = 2ⁿ ⇒ (6.4 × 10⁻⁴)/(5 × 10⁻⁶) = 128 = 2⁷

2. Count half-lives. Since 128 = 2⁷, the activity has halved n = 7 times. Each half-life is 5 days, so the time taken is t = 7 × 5 = 35 days.
3. So. The activity falls to 5 × 10⁻⁶ curie after 35 days, option (d).

The idea to keep. When the starting and final activities differ by a power of 2, find that power n. The time taken is n times the half-life, with no logarithms needed.

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