A sample of a radioactive isotope has an initial activity of . Exactly later, its activity drops to — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A sample of a radioactive isotope has an initial activity of $28\text{ dpm}$. Exactly $30\text{ minutes}$ later, its activity drops to $14\text{ dpm}$. What is the decay constant ($\lambda$) of this isotope? (Use $\ln 2 \approx 0.693$).
Answer: B
💡 Solution & Explanation
The activity halves from $28$ to $14\text{ dpm}$ in $30\text{ min}$, meaning the half-life $T_{1/2} = 30\text{ minutes}$. The decay constant $\lambda = 0.693 / T_{1/2} = 0.693 / 30 = 0.0231\text{ min}^{-1}$.
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