The half-life of a radioactive material undergoing \( \beta \)-decay is 12.5 years. What fraction the material remains undecayed after 25 years?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{4} \)
In every half-life the undecayed amount falls to half, whatever the type of decay. After \( n \) half-lives
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n}, \qquad n = \frac{t}{T_{1/2}} \)
\( \displaystyle n = \frac{25\,\mathrm{years}}{12.5\,\mathrm{years}} = 2 \)
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{2} = \frac{1}{4} \)