Question

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ratio of initial active nuclei of 2 different samples is 2:3 .Their half lives are 1 and 2 hours respectively ratio of active nuclei at the end of 6 hours will be????
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Answer 1

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Answer 2

Answer:

The ratio of remaining active nuclei in the sample after 6 hours is 1:12.

Explanation:

Given that,

The ratio of initial active nuclei of 2 different samples is 2:3.

Their half lives are 1 and 2 hours respectively

Let us consider the two samples to be A and B.

Half life of A $t_{\dfrac{1}{2}}= 1 hour$

Half life of B $t_{\dfrac{1}{2}}= 2 hour$

We know that,

The number of nuclei in terms of half life

$N =\dfrac{N_{0}}{2^(\dfrac{t}{t_{\dfrac{1}{2}}})}$

The remaining active nuclei in the sample A after 6 hours

$N_{A}=\dfrac{N_{0}}{2^{\dfrac{6}{1}}}$

$N_{A}=\dfrac{N_{0}}{64}$

$N_{A}=\dfrac{1}{32}$

The remaining active nuclei in the sample B after 6 hours

$N_{B}=\dfrac{N_{0}}{2^{\dfrac{6}{2}}}$

$N_{B}=\dfrac{N_{0}}{8}$

$N_{B}=\dfrac{3}{8}$

The ratio of remaining active nuclei in the sample after 6 hours is

$\dfrac{N_{A}}{N_{B}}=\dfrac{8}{3\times32}$

$\dfrac{N_{A}}{N_{B}}=\dfrac{1}{12}$

Hence, The ratio of remaining active nuclei in the sample after 6 hours is 1:12.