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A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.

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प्रश्न

A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant. 

योग
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उत्तर

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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