Question

A newly discovered element, Y, 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? 267.9 u 268.1 u 268.9 u 269.1 u

Answer 1

(0.878)(267.8) + (.122)(269.9) = 268.1 g/mol (B)

Answer 2

Answer :  The average atomic mass of this element is, 268.1 u

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:

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

For isotope-1 :

Mass of isotope-1 = 267.8 amu

Fractional abundance of isotope-1 = 87.8 % = 0.878

For isotope-2 :

Mass of isotope-2 = 269.9 amu

Fractional abundance of isotope-2 = 12.2 % = 0.122

Putting values in equation 1, we get:

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

$\text{Average atomic mass }=268.1u$

Thus, the average atomic mass of this element is, 268.1 u