To calculate the relative atomic mass (\(A_r\)) of magnesium, we can use the formula:
\[ A_r = \frac{(mass \ of \ isotope_1 \times abundance_1) + (mass \ of \ isotope_2 \times abundance_2) + (mass \ of \ isotope_3 \times abundance_3)}{100} \]
Given the isotopes and their abundances:
- \(^{24}_{12}\text{Mg}\): mass = 24, abundance = 79.0%
- \(^{25}_{12}\text{Mg}\): mass = 25, abundance = 10.0%
- \(^{26}_{12}\text{Mg}\): mass = 26, abundance = 11.0%
Now we plug in the numbers:
\[ A_r = \frac{(24 \times 79.0) + (25 \times 10.0) + (26 \times 11.0)}{100} \]
Calculating each contribution:
- For \(^{24}\text{Mg}\): \(24 \times 79.0 = 1896\)
- For \(^{25}\text{Mg}\): \(25 \times 10.0 = 250\)
- For \(^{26}\text{Mg}\): \(26 \times 11.0 = 286\)
Now sum these up:
\[ A_r = \frac{1896 + 250 + 286}{100} = \frac{2432}{100} = 24.32 \]
Thus, the relative atomic mass (\(A_r\)) of magnesium is approximately:
\[ A_r = 24.32 \]
Rounding to three significant figures, we obtain:
\[ \mathbf{24.3} \]