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Question

What is the half life of a radioactive substance 87.5% of any given amount of the substance disintegrate in 40 minutes?

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Solution

1st Order Reaction

$k = \frac{2.303}{t} l o g \frac{[100]}{[100 - x]}$

$k = \frac{2.303}{40} l o g \frac{[100]}{[12.5]}$

$k = 5.2 \times 10^{- 2} {m i n}^{- 1}$

Half Life = $\frac{0.693}{k}$ = $\frac{0.693}{5.2 \times 10^{- 2}}$ = 13.3 min

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