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Question
A radioactive nucleus has a decay constant λ = 0.3465 (day)–1. How long would it take the nucleus to decay to 75% of its initial amount?
Solution
According to the decay law, we have:
\[R = R_0 e^{- \lambda t} \]
\[ \Rightarrow \frac{R_0 \times 75}{100} = R_0 e^{- 0 . 3465t} \]
\[ \Rightarrow \frac{4}{3} = e^{0 . 3465t} \]
\[ \therefore t = 0 . 823 \text { days }\]
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