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The half life of $_{84}^{209} P_{o}$ 103 years. The time taken for 100g sample of $_{84}^{209} P_{o}$ to decay to 3.125g is

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515 years

3296 years

$103 \sqrt{2}$ years

1648 years

answer is D.

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Detailed Solution

Half life of sample = 103 years

Initial amount $N_{0} = 100 g$

Final N = 3.125g

$N = \frac{N_{0}}{2^{n}} \Rightarrow \frac{100}{3.125} = 2^{n} \Rightarrow 2^{n} = 32$

$\Rightarrow n = 5$

$t = n T$

$t = 5 (103)$

$t = 515 y e a r s$

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