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  4. Polonium has a half-life of 140 days. If we take 20 g of polonium initially then the amount of it that remains after 280 days is

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Q. Polonium has a half-life of $140$ days. If we take $20\,g$ of polonium initially then the amount of it that remains after $280$ days is

J & K CETJ & K CET 2013Nuclei

Solution:

After n-half lines, quantity of radiatioactive substance left is
$N=N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
Given, $T_{1 / 2}=140$ days,
$t=28$ days, $N_{0}=20\, g$
$\therefore N=20\left(\frac{1}{2}\right)^{\frac{280}{140}}$
$=\frac{20}{4}=5\, g$