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Question

Two radioactive substances A and B are present as, [A] = 8[B] and t1/2 of A = 10 minutes; t1/2 of B = 20 minutes. If they start decaying at the same time then after how much time concentration of both would be same:

A
20 min
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B
40 min
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C
60 min
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D
200 min
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Solution

The correct option is C 60 min
For the radioactive elements which follow first order kinetics t1/2 is the time in which the concentration becomes half of the initial concentration.
For example X has initial concentration[X] than [X]t1/2[X]/2t1/2[X]/4
So for substance A which has concentration [A]=8[B]
So it decay will like this [A]=8[B]10min4[B]10min2[B]10min[B]10min[B]/210min[B]/410min[B]/8.............
Same for B [B]20min[B]/220min[B]/420min[B]/8.............

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