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  4. A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope ?

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Q. A radioactive isotope having a half - life period of $3$ days was received after $12$ days. If $3g$ of the isotope is left in the container, what would be the initial mass of the isotope ?

JEE MainJEE Main 2013Chemical Kinetics

Solution:

Given $tm = 3$
Total time $T= 12$
No. of half lives (n)=$\frac{12}{3}=4$
$\left(\frac{1}{2}\right)^{n} =\frac{N}{N_{0}}$
$\therefore \left(\frac{1}{2}\right)^{4} =\frac{3}{N_{0}}$
$\frac{3}{N_{0}} =\frac{1}{16}$
$N_{0} =48 \,g$