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Question

Two radioactive nuclide P and Q have their decay constant in the ratio 3: 2 . One mole of each is taken separately and allowed to decay for a time interval of three times of half-life of A. If 0.2 mole of P are left, what mole of Q will be left? (multiply X×100)

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Solution

Let decay constant λP and λQ be 3a and 2a respectively.
t1/2ofP=0.6933a;t1/2ofQ=0.6932a
T=3×t1/2ofP=3×0.6933a=0.693a
T=2.303λlogaax
ForP:0.693a=2.3033alog1nP
ForQ:0.693a=2.3032alog1nQ
=log1nPlog1nQ=32
or, log1nP=32log1nQ
log1nP=log(1nQ)3/2
or, nP=(nQ)2/3
if nP=0.2,thennQ=0.09 mole of Q will be left.
0.09×100=9.

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