Question

A newly discovered element, X, has two naturally occurring isotopes. 87.8 percent of the sample is an isotope with a mass of 267.8 u, and 12.2 percent of the sample is an isotope with a mass of 269.9 u. What is the weighted average atomic mass for this element?

Answer 1

The weighted average atomic mass (m) of the newly discovered element X is the sum of the products of its isotopes percentage and mass.                    
m = (0.935) x (268.9 u) + (0.065) x (269.9 u) = 268.965 u
Thus, the weight of the atom is approximately 269.0 u.

Answer 2

Answer: The average atomic mass of the given element X will be 268.06 u.

Explanation:

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

Formula that is used to calculate the 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)

We are given:

Mass of isotope 1 = 267.8 u

Percentage abundance of isotope 1 = 87.8 %

Fractional abundance of isotope 1 = 0.878

Mass of isotope 2 = 269.9 u

Percentage abundance of isotope 2 = 12.2 %

Fractional abundance of isotope 2 = 0.122

Putting values in equation 1, we get:

$\text{Average atomic mass of X}=[(267.8\times 0.878)+(269.9\times 0.122)]$

$\text{Average atomic mass of X}=268.06u$

Hence, the average atomic mass of the given element X will be 268.06 u.