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Question

# 84Po218(t1/2=3.05min)decay to 82Pb214(t1/2=2.68min) by α -emission,while Pb214 is a β -emitter. In an experiment starting with 1gm atom of pure Po218,how much time would be required for the number of nuclei of 82Pb214 to reach maximum?

A
4.125 min
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B
8.25 min
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C
41.25 min
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D
None of these
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Solution

## The correct option is B 4.125 minFor 1st process rate constant K1 = 0.6933.05 min−1=0.227min−1For 2nd process rate constant K2 = 0.6932.68 min−1=0.259min−1tmax = 1(K1−K2)lnK1K2=10.227−0.259)ln2.683.05=4.125 min

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