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A radioactive nuclei A decays into a stable nuclei B with half life 750 years. In an old sample ratio of number of nuclei of A to the number of nuclei of B is 1:7. Age of the sample is 500 n years. Find the value of n. Assume that initially equal number of nuclei of A and B were present in the sample.

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answer is 3.

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Detailed Solution

$A \to B t = 0 N_{0} N_{0} t = t N 2 N_{0} - N \frac{N}{2 N_{0} - N} = \frac{1}{7} \Rightarrow N = \frac{N_{0}}{4}$

2 half lives : 1500 years

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