A radioactive substance decays to ( 1/16 )ᵗʰ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.

Solution

Physics sir · 3 steps

Write 1/16 as a power of one-half: that power tells you how many half-lives fit into 80 days.

1. Activity and half-lives. Activity falls exactly like the number of nuclei. After n half-lives it is A = A₀ (1/2)ⁿ.

   A/A₀ = 1/16 = (1/2)⁴ ⇒ n = 4

2. Share out the time. Four half-lives take 80 days in total. So one half-life is T_(1/2) = 80/4 = 20 days.
3. So. The half-life of the substance is 20 days.

The common slip: 5. Dividing 80 by 16 instead of by the number of halvings gives 5 days. The fraction 1/16 means 4 halvings, not 16.

The idea to keep. When the remaining fraction is a neat power of one-half, count the halvings: 1/2ⁿ means n half-lives. Then divide the total time by n.

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