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Two radioactive substances have half-liv...

Two radioactive substances have half-lives `T` and `2T`. Initially, they have equal number of nuclei. After time `t=4T`, the ratio of their number of nuclei is `x` and the ratio of their activity is `y`. Then,

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The given time , 1 hour is `3 t_(1//2) = //2^(3) = 1//8`
The fraction of A left after `3 t_(1//2) = 1//2^(3) = 1//8`
(a) The ratio of moles left ` = 1//8: 1//4 = 1: 2`
(b) The ratio of activities ` = (lambda_(A)N_(A))/(lambda_(B)N_(B)) = (N_(A)(t_(1//2))_(B))/(N_(B)(t_(1//2))_(A)) = ((1//8)xx30)/((1//4)xx20) = 3:4`
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