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A counter rate metre is used to measure ...

A counter rate metre is used to measure the activity of a radioactive sample. At a certain instant, the count rate was recorded as 400 counters per minute. Five minutes later, the count recorded was 200 counts per min. Calculate the decay and half-period of the sample.

Text Solution

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Let `N_(0)` and `N` be the number rate atoms of the radioactive substance present at the start and after 5 min, respectively.
Rate of disintegration at the start `= KN_(0) = 400`
Dividing both, `(KN_(0))/(KN) = (400)/(200)`
or `(N_(0))/(N) = 2.00`
We know that `K = (2.303)/(t) log (N_(0))/(N)`
` K = (2.303)/(5) log 2.00 = 0.138 "min"^(-1)`
Half life period `= (0.693)/(K) = (0.693)/(0.138) = 5.0` min
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