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Q.

The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. 5 min later, the rate becomes 2700 min-1. Then, the half-life of the sample (in min) is…….. ln475200=0.56

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answer is 6.13.

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Detailed Solution

From the relation,R=R0e−λt  (Here, R= activity of sample)Substituting the values, we have    2700=4750e−5λ∴5λ=ln⁡47502700=0.56∴λ=0.113min−1Half-life of the sample,t1/2=ln⁡2λ=0.6930.113=6.132min
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The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. 5 min later, the rate becomes 2700 min-1. Then, the half-life of the sample (in min) is…….. ln475200=0.56