# Q.13.23 In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are  $_{12}^{24}\textrm{Mg}(23.98504\; u)$, $_{12}^{25}\textrm{Mg}(24.98584\; u)$ and $_{12}^{26}\textrm{Mg}(25.98259\; u)$. The natural abundance of is 78.99% by mass. Calculate the abundances of other two isotopes.

S Sayak

Let the abundances of $_{12}^{25}\textrm{Mg}$ and $_{12}^{26}\textrm{Mg}$ be x and y respectively.

x+y+78.99=100

y=21.01-x

The average atomic mass of Mg is 24.312 u

$\\24.312=\frac{78.99\times 23.98504+x\times 24.98584+(100-x)\times 25.98259}{100}\\ x\approx 9.3\\ y=21.01-x\\ y=21.01-9.3\\ y=11.71$

The abundances of $_{12}^{25}\textrm{Mg}$ and $_{12}^{26}\textrm{Mg}$  are 9.3% and 11.71% respectively

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