Question

The natural distribution of the isotopes of a hypothetical element is 60.795% at a mass of 281.99481 u, 22.122% at a mass of 283.99570 u, and the remainder has a mass of 286.99423 u. Calculate the atomic mass of the element

Answer 1

Answer: The average atomic mass of the element is 283.291 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:

Mass of isotope 1 = 281.99481 amu

Percentage abundance of isotope 1 = 60.795 %

Fractional abundance of isotope 1 = 0.60795

• For isotope 2:

Mass of isotope 2 = 283.99570 amu

Percentage abundance of isotope 2 = 22.122 %

Fractional abundance of isotope 2 = 0.22122

• For isotope 3:

Mass of isotope 3 = 286.99423 amu

Percentage abundance of isotope 3 = [100 - (60.795 + 22.122)] = 17.083 %

Fractional abundance of isotope 1 = 0.17083

Putting values in equation 1, we get:

$\text{Average atomic mass of element}=[(281.99481\times 0.60795)+(283.99570\times 0.22122)+(286.99423\times 0.17083)]\\\\\text{Average atomic mass of element}=283.291amu$

Hence, the average atomic mass of the element is 283.291 amu