After how many half lives a radioactive substance will decay to 6.25% of its original value:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Four half lives
In each half-life the amount of a radioactive substance falls to half, so after n half-lives \( N = N_0\left(\frac{1}{2}\right)^{n} \). Here the remaining fraction is 6.25% = 0.0625 = \( \frac{1}{16} \).
\( \displaystyle \left(\frac{1}{2}\right)^{n} = \frac{1}{16} = \left(\frac{1}{2}\right)^{4} \Rightarrow n = 4 \)
(100% → 50% → 25% → 12.5% → 6.25%, four halvings.)