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Q.

In a certain hypothentical radioactive decay process, species A decays into species B and species B decays into species C according to the reactions :A→2B+ particles +energy B→2C+ particles +energy The decay constant for species is λ1=1sec−1 and that for the species B is  λ2=100sec−1 .Initially 104 moles of species of A were present while there was none of B and C. It was found that species B reaches its maximum number at a time t0=2 ln (10)sec. Calculate the value of maximum number of moles of B.

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a

1

b

2

c

5

d

4

answer is B.

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Detailed Solution

dNAdt=λ1NA dNBdt=2λ1NA−λ2NB ,NB =maximum ⇒dNBdt=0⇒2λ1NA=λ2NBmax ⇒NBmax=2λ1λ2NA⇒NBmax=2λ1λ2N0e−λ1t=2
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