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The count rate meter is used to measure ...

The count rate meter is used to measure that activity of a given amount of a radio active element. At one instant, the meter shows 475 counts/minute. Exactly 5 minutes later, is shown 270 counts/minute then
Half life of the sample is (in minute)

Text Solution

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Initial activity `A_(i) = (-dN)/(dt)|_(t=0) = lambdaN_(0) = 4750"….."(i)` , Final activity `A_(f) = (-dN)/(dt) |_(t=5) = lambdaN = 2700"……"(ii)`
Dividing (i) by (ii), we get `(4750)/(2700) = (N_(0))/(N_(t))`
The decay constant is given by `lambda = (2.303)/(t) "log"(N_(0))/(N_(t)) = (2.303)/(5) "log" (4750)/(2700) = 0.113 "min"^(-1)`
Half-life of the sample is `T = (0.693)/(lambda) = (0.693)/(0.113) = 6.14 min`
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