The rate constant for the radioactive decay of an isotope is 2.31 × 10−4 year−1. Its half-life is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 × 103 years
Radioactive decay follows first order kinetics, so the half-life comes straight from the rate constant:
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)
\( \displaystyle t_{1/2}=\frac{0.693}{2.31\times10^{-4}\,\mathrm{year^{-1}}} \)
\( \displaystyle t_{1/2}=3\times10^{3}\,\mathrm{years} \)
The half-life is 3 × 103 years (3000 years).