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Question
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
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Solution
Given: t1/2 = 110 min, t = 20 min
To find: Fraction of 18F sample that decays
Formulae:
- `lambda = 0.693/"t"_(1//2)`
- `lambda = 2.303/"t" log_10 ("N"_0/"N")`
Calculation: `lambda = 0.693/"t"_(1//2) = 0.693/110 = 0.0063 "min"^-1`
`lambda = 2.303/"t" log_10 ("N"_0/"N")`
∴ `log_10 ("N"_0/"N") = (lambda xx "t")/(2.303) = (0.0063 xx 20)/2.303 = 0.0547`
`("N"_0/"N") = 1.1342`
∴ Fraction remaining undecayed = `"N"/"N"_0 = 1/1.1342 = 0.882`
∴ Fraction of 18F sample that decays = 1 - 0.882 = 0.118
Fraction of 18F sample that decays in 20 minutes is 0.118.
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