Question

Magnesium has three naturally occurring isotopes(Mg-24, Mg-25, and Mg-26). The atomic mass and natural abundance of Mg-24 are 23.9850amu and 79 %, respectively. The atomic mass and natural abundance of Mg-25 are 24.9858amu and 10 %, respectively.

Find the natural abundance of Mg-26.

Express your answer using two significant figures.

Find the atomic mass of Mg-26.

Express your answer using two significant figures.

Answer 1

Answer: The percentage abundance of Mg-26 is 11 % and the atomic mass of Mg-26 isotope is 26. 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)

Let the mass of Mg-26 isotope be 'x' amu

• For isotope 1 (Mg-24) :

Mass of isotope 1 = 23.9850 amu

Percentage abundance of isotope 1 = 79 %

Fractional abundance of isotope 1 = 0.79

• For isotope 2 (Mg-25) :

Mass of isotope 2 = 24.9858 amu

Percentage abundance of isotope 2 = 10 %

Fractional abundance of isotope 2 = 0.10

• For isotope 3 (Mg-26) :

Mass of isotope 3 = x amu

Percentage abundance of isotope 3 = [100 - 79 - 10] % = 11 %

Fractional abundance of isotope 3 = 0.11

Average atomic mass of magnesium = 24.305 amu

Putting values in equation 1, we get:

$24.305=[(23.9850\times 0.79)+(24.9858\times 0.10)+(x\times 0.11)]$

$x=25.984amu=26.amu$

Hence, the percentage abundance of Mg-26 is 11 % and the atomic mass of Mg-26 isotope is 26. amu