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Answer :
For a first-order reaction, it takes approximately 10 half-lives to reach 99.9% completion, and since one half-life is given as t seconds, the time required for 99.9% completion is 10 times t (10t).
The question pertains to a first-order reaction and how long it takes for a certain percentage of completion to be achieved. In a first-order reaction, the time it takes for the concentration of a reactant to decrease to half is defined as the half-life (t1/2). If t seconds represent the half-life of the reaction, then each subsequent half-life will result in halving the remaining reactant concentration.
After the first half-life (t seconds), 50% of the reactant remains. After the second half-life (another t seconds, totaling 2t seconds), 25% remains. This pattern continues such that after n half-lives, the fraction of reactant remaining is (1/2)n. For 99.9% completion, the remaining reactant is 0.1%, which means (1/2)n = 0.001. Solving logarithmically, we find that n is approximately 10. Thus, the time required is 10t, which correlates to option B.
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