The relative atomic mass (A_r) of atoms is the average mass of all the different isotopes of an element (taking into account the amount of each isotopes) on a scale weere ^12C atoms have mass of exactly 12.

Element Magnesium isotopes 24 12 Mg 25 12 Mg 26 12 Mg Abundance 79.0% 10.0% 11.0% Relative atomic mass (A_r) to (3sf) ___

1 answer

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:

\[ \mathbf{24.3} \]