Question

An imaginary element (X) on Mars is composed of three isotopes, 10.68% of isotope X-95 with a mass of 95.0 amu, 16.90% of isotope X-96 with a mass of 96.0 amu, and 72.42% of isotope X-97 with a mass of 97.0 amu. Calculate the atomic mass (in amu) of the element. Type in your answer with 3 significant figures.

Answer 1

Answer: The average atomic mass of element X is 96.6 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 isotope 1 (X-95):

Mass of isotope 1 = 95.0 amu

Percentage abundance of isotope 1 = 10.68 %

Fractional abundance of isotope 1 = 0.1068

• For isotope 2 (X-96):

Mass of isotope 2 = 96.0 amu

Percentage abundance of isotope 2 = 16.90 %

Fractional abundance of isotope 2 = 0.1690

• For isotope 3 (X-97):

Mass of isotope 3 = 97.0 amu

Percentage abundance of isotope 3 = 72.42 %

Fractional abundance of isotope 3 = 0.7242

Putting values in equation 1, we get:

$\text{Average atomic mass of X}=[(95\times 0.1068)+(96\times 0.1690)+(97\times 0.7242)]$

$\text{Average atomic mass of X}=96.6amu$

Hence, the average atomic mass of element X is 96.6 amu.