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Q.

A piece of substance consists of two radioactive elements A and B. Initial ratio of number of active nuclei of A and B is 4 : 1. Half life of element A is T and that of element B is 2T. After what time number of active nuclei of A will be equal to that of B?

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a

2T

b

T

c

8T

d

4T

answer is C.

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Detailed Solution

Initial number of active nucleus of A = 4N0

Initial number of active nucleus of B = N0

After time t, NA=4N0(2)t/T  and NB=N0(2)t/T

When NA=NB , 4N0(2)t/T=N0(2)t/2T⇒(2)t2T+2=(2)t/T

⇒tT=t2T+2⇒t=4T

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