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Question

At radioactive equilibrium, the ratio of two atoms A and B are 3.1×109:1. If half life of 'A' is 2×1010 yrs, what is half life of 'B'?

A
6.45 yrs
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B
4.65 yrs
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C
5.46 yrs
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D
5.64 yrs
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Solution

The correct option is B 6.45 yrs
Specific radioactivity 'a' is defined as radioconductivity per unit mass at the radionuclide.
Half life is related by equation
T1/2=(NA)ln2a×m(T1/2)A(T1/2)B=(NA)A(NB)B2×1010(T1/2)B=3.1×1092.0×10103.1×109=(T1/2)B(T1/2)B=6.45years.

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