A radioactive sample has a half life of 12 years. The fraction of sample that will decay in 24 years is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{3}{4} \)
After a time t the undecayed fraction of a radioactive sample is \( N/N_0 = (1/2)^{t/T_{1/2}} \), and the fraction that has decayed is one minus this.
\( \displaystyle \frac{t}{T_{1/2}} = \frac{24}{12} = 2 \text{ half-lives} \)
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{2} = \frac{1}{4} \)
\( \displaystyle \text{fraction decayed} = 1-\frac{1}{4} = \frac{3}{4} \)