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Question

Consider the parallel first order reactions given above.
The half-life for the decay of $$A$$ is _________ hrs.
662121_cf41eee5d4214b3c9ea07527f52769fd.png


A
1
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B
3
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C
4
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D
12
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Solution

The correct option is B $$3$$
For parallel first order reaction,
$$-\frac{dA}{dt}=(k_1+k_2)[A]=k[A]$$
$$t_{1/2}=\frac{In2}{k}=\frac{In2}{k_1+k_2}$$
$$=\frac{In2}{\frac{In2}{(t_{1/2})_1}+\frac{In2}{(t_{1/2})_2}}=\frac{(t_{1/2})_1\times (t_{1/2})_2}{(t_{1/2})_1+(t_{1/2})_2}$$
$$=\frac{4\times 12}{4+12}$$ =3 hrs

Chemistry

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