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  4. The half-life of radioactive element is 600 yr. The fraction of sample that would remain after 3000 yr is

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Q. The half-life of radioactive element is $600 \,yr$. The fraction of sample that would remain after $3000 \,yr$ is

AIIMSAIIMS 2012

Solution:

We know that
$n = \frac{1}{T}$
Given, $n =\frac{1}{T} $
$t =3000\, yr$
$T =600 \,yr $
$n =\frac{3000}{600}=5$
Then, $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{5}=\frac{1}{32}$