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Question
The half-life of radon is 3.82 d. By what time would 99.9% of radon will be decayed?
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Solution
Given: t1/2 = 3.82 d, N0 = 100 N = 100 - 99.9 = 0.1
To find: t
Formulae:
- `lambda = 0.693/"t"_(1//2)`
- t = `2.303/lambda log_10 ("N"_0/"N")`
Calculation:
- `lambda = 0.693/"t"_(1//2) = 0.693/3.82 = 0.1814 "d"^-1`
- t = `2.303/lambda log_10 ("N"_0/"N")`
`= 2.303/0.1814 xx log_10 (100/0.1)`
`= 2.303/0.1814 log_10 (1000)`
t = 38.087 d ≈ 38.1 d
Time taken for 99.9% of radon to be decayed is 38.1 d.
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