Answer :
To find the relative atomic mass of magnesium (Mg), we need to take into account the natural abundances and the atomic masses of its isotopes. The steps are as follows:
1. Convert the percentages of abundance into decimals:
- The abundance of \(^{24}\text{Mg}\) is 78.99%, which is \(0.7899\) in decimal form.
- The abundance of \(^{25}\text{Mg}\) is 10.00%, which is \(0.1000\) in decimal form.
- The abundance of \(^{26}\text{Mg}\) is 11.01%, which is \(0.1101\) in decimal form.
2. Multiply the atomic mass of each isotope by its abundance:
- For \(^{24}\text{Mg}\): \(0.7899 \times 23.98504 = 18.951882996\)
- For \(^{25}\text{Mg}\): \(0.1000 \times 24.98584 = 2.498584\)
- For \(^{26}\text{Mg}\): \(0.1101 \times 25.98259 = 2.854583259\)
3. Sum these values to get the relative atomic mass of Mg:
- \(18.951882996\) (from \(^{24}\text{Mg}\))
- \(2.498584\) (from \(^{25}\text{Mg}\))
- \(2.854583259\) (from \(^{26}\text{Mg}\))
The total sum is \(18.951882996 + 2.498584 + 2.854583259 = 24.305050255\).
Thus, the relative atomic mass of magnesium (Mg) is [tex]\(24.305050255 \, \text{amu}\)[/tex].
1. Convert the percentages of abundance into decimals:
- The abundance of \(^{24}\text{Mg}\) is 78.99%, which is \(0.7899\) in decimal form.
- The abundance of \(^{25}\text{Mg}\) is 10.00%, which is \(0.1000\) in decimal form.
- The abundance of \(^{26}\text{Mg}\) is 11.01%, which is \(0.1101\) in decimal form.
2. Multiply the atomic mass of each isotope by its abundance:
- For \(^{24}\text{Mg}\): \(0.7899 \times 23.98504 = 18.951882996\)
- For \(^{25}\text{Mg}\): \(0.1000 \times 24.98584 = 2.498584\)
- For \(^{26}\text{Mg}\): \(0.1101 \times 25.98259 = 2.854583259\)
3. Sum these values to get the relative atomic mass of Mg:
- \(18.951882996\) (from \(^{24}\text{Mg}\))
- \(2.498584\) (from \(^{25}\text{Mg}\))
- \(2.854583259\) (from \(^{26}\text{Mg}\))
The total sum is \(18.951882996 + 2.498584 + 2.854583259 = 24.305050255\).
Thus, the relative atomic mass of magnesium (Mg) is [tex]\(24.305050255 \, \text{amu}\)[/tex].
