The half life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 days
In each half-life the number of undecayed nuclei falls to half. If \( 3/4 \) of the substance has disintegrated, the amount remaining is \( 1/4 \) of the initial value.
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n} = \frac{1}{4} \;\Rightarrow\; n = 2 \)
\( \displaystyle t = n\,T_{1/2} = 2 \times 10\,\mathrm{days} = 20\,\mathrm{days} \)