AP EAMCET · Chemistry · Chemical Kinetics
\(10 \mathrm{~g}\) of a radioactive element is disintegrated to \(1 \mathrm{~g}\) in 2.303 minutes. What is the half-life (in minutes) of that radioactive element?
- A \(1 / 0.693\)
- B \(6.93\)
- C \(1\)
- D \(0.693\)
Answer & Solution
Correct Answer
(D) \(0.693\)
Step-by-step Solution
Detailed explanation
Radioactive disintegration is first order reaction \[ \begin{aligned} k & =\frac{2303}{t} \log \frac{a}{a-x} \\ & =\frac{2.303}{2.303} \log \frac{10}{1} \\ k & =1 \\ t_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{1} \\ & =0.693 \mathrm{~min} \end{aligned} \]
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