Question

The naturally occurring isotopes of magnesium are magnesium-24. magnesium-25, and magnesium-26. Magnesium-24 has an abundance of 78.994% and a mass of 23.985 amu. Magnesium-25 has an abundance of 10.001% and a mass of 24.986 amu. Magnesium-26 has an abundance of 11.013% and a mass of 25.983 amu. Calculate the average atomic mass of magnesium.

Answer 1

Answer: The average atomic mass of magnesium is 24.307 amu.  

Explanation:

Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.  

Formula used to calculate average atomic mass follows:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$   .....(1)

• For $_{12}^{24}\textrm{Mg}$ isotope:

Mass of $_{12}^{24}\textrm{Mg}$ isotope = 23.985 amu

Percentage abundance of $_{12}^{24}\textrm{Mg}$ isotope = 78.994 %

Fractional abundance of $_{12}^{24}\textrm{Mg}$ isotope = 0.78994

• For $_{12}^{25}\textrm{Mg}$ isotope:

Mass of $_{12}^{25}\textrm{Mg}$ isotope = 24.986 amu

Percentage abundance of $_{12}^{25}\textrm{Mg}$ isotope = 10.001 %

Fractional abundance of $_{12}^{25}\textrm{Mg}$ isotope = 0.10001

• For $_{12}^{26}\textrm{Mg}$ isotope:

Mass of $_{12}^{26}\textrm{Mg}$ isotope = 25.983 amu

Percentage abundance of $_{12}^{26}\textrm{Mg}$ isotope = 11.013 %

Fractional abundance of $_{12}^{26}\textrm{Mg}$ isotope = 0.11013

Putting values in equation 1, we get:  

$\text{Average atomic mass of magnesium}=[(23.985\times 0.78994)+(24.986\times 0.10001)+(25.983\times 0.11013)]$

$\text{Average atomic mass of magnesium}=24.307amu$

Hence, the average atomic mass of magnesium is 24.307 amu.