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 λ$$1=1sec$$−$$1$$ and that for the species B is λ$$2=100sec$$−$$1$$ .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.

Question

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 λ$$1=1sec$$−$$1$$ and that for the species B is  λ$$2=100sec$$−$$1$$ .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.

Infinity Learn · Accepted Answer

$$dNAdt=$$λ$$1NA$$ $$dNBdt=2$$λ$$1NA$$−λ$$2NB$$ ,NB $$=maximum$$ ⇒$$dNBdt=0$$⇒$$2$$λ$$1NA=$$λ$$2NBmax$$ ⇒$$NBmax=2$$λ$$1$$λ$$2NA$$⇒$$NBmax=2$$λ$$1$$λ$$2N0e$$−λ$$1t=2$$

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