Final answer:
To calculate the average atomic mass of magnesium, multiply the percentage of each isotope by its atomic mass and sum the results. This weighted average calculation, which accounts for the relative abundances of Mg-24, Mg-25, and Mg-26 isotopes, provides the average atomic mass of the element.
Step-by-step explanation:
Calculating the Average Atomic Mass of Magnesium
To calculate the average atomic mass of magnesium, we need to know the percentage of each isotope present in the sample and the atomic mass of each isotope. Since magnesium has isotopes of Mg-24, Mg-25, and Mg-26 with given percentages and atomic masses, we apply a weighted average calculation. The formula to calculate the average atomic mass is:
Atomic mass = (% of 24Mg × mass of 24Mg) + (% of 25Mg × mass of 25Mg) + (% of 26Mg × mass of 26Mg)
Using the given data in the question, the calculation would look like this:
- 78.70% of 24Mg atoms (mass 23.98 amu)
- 10.13% of 25Mg atoms (mass 24.99 amu)
- 11.17% of 26Mg atoms (mass 25.98 amu)
After multiplying each percentage by its corresponding mass in atomic mass units (amu) and adding them together, we get the average atomic mass for magnesium. This process is known as calculating a weighted average based on relative abundance.