Average atomic mass =\frac{\Sigma\text{isotope abundance * isotope mass }}{\Sigma\text{ isotope abundance }}
= \frac{\Sigma (m_i \eta_i)}{\Sigma \eta_i}
Step 1: Calculating the isotopes abundances
Given that
Average atomic mass magnesium = 24.313 u
Mass of ^{24}_{12} Mg = 23.98504 u
Mass of ^{25}_{12} Mg = 24.98584 u
Mass of ^{26}_{12} Mg = 25.98259 u
Abundance of ^{24}_{12} Mg = 78.99 %
Abundance of ^{25}_{12} Mg = x%
Abundance of ^{26}_{12} Mg = y% = 78.99 % + x% + y%= 100%
y% = 100% - 78.99 % - x% = 21.01% - x%
Substituting the all the values in the average atomic mass formula.
Average atomic mass = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{78.99 + x + 21.01 - x }
24.313 = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{100}
24.313 = \frac{1894.578 + 545.894 + x(24.98584 - 25.98259)}{100}
x = \frac{2440.472 - 2431.2}{0.99675}
x = 9.30
Abundance of ^{26}_{12} Mg = 21.01 - x = 21.01 - 9.30 = 11.71
Hence, Abundance of ^{25}_{12} Mg is 9.30% and Abundance of ^{26}_{12} Mg is 11.71%