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Q.

The half-life of ${}^{215}{At}$ is $100 μs$ . The time taken for the radioactivity of a sample of ${}^{215}{At}$ to decay to 1/16^th of its initial value is

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a

$400 μs$

b

$40 μs$

c

$300 μs$

d

$6.3 μs$

answer is A.

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Detailed Solution

$N = \frac{N_{0}}{2^{n}} \Rightarrow \frac{N_{0}}{16} = \frac{N_{0}}{2^{n}} \Rightarrow n = 4$

$∴ t = {nT}_{1 / 2} = 4 (100) = 400 μs .$

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