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?

Question

Infinity Learn · Accepted Answer

Initial number of active nucleus of A $$=$$ $$4N0Initial$$ number of active nucleus of B $$=$$ $$N0After$$ time t, $$NA=4N0(2)t/T$$  and $$NB=N0(2)t/TWhen$$ $$NA=NB$$ , $$4N0(2)t/T=N0(2)t/2T$$⇒$$(2)t2T+2=(2)t/T$$⇒$$tT=t2T+2$$⇒$$t=4T$$

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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