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Question
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
Solution
Here, `("N"("t"))/"N" = 1/10` and t = 56 days
We have, `("N"("t"))/"N"_0 = "e"^{-lambda"t"}`
∴ `1/10 = "e"^{-lambda"t"}`
∴ `"e"^{lambda"t"} = 10`
∴ `lambda"t" = log_"e"10`
∴ `lambda = (log_"e"10)/"t"`
= `(2.303 xx log 10)/56`
= `2.303/56`
= antilog {log(2.303) − log (56)}
= antilog {0.3623 − 1.7481}
= antilog {`overline2` .6142}
= 4.113 × 10−2 per day
The decay constant is 4.113 × 10−2 per day.
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