Calculate Average Atomic Mass from Isotope Abundance and Mass

Published on March 18, 2026

Word-Problem

Determine the weighted average atomic mass of element Lz using the given fractional abundances (5/8 and 3/8) and the masses of its two isotopes (319.9 amu and 322.0 amu). This requires applying the weighted average formula.

Question

Answer

Here is the step-by-step solution to find the average atomic mass of the fictitious element Lz.
1. Identify the given information:
  • The element Lz has two common isotopes.
  • Isotope 1: Mass ( ) = .
  • Fractional Abundance of Isotope 1 ( ): .
  • Isotope 2: Mass ( ) = .
  • Fractional Abundance of Isotope 2 ( ): The rest of the isotopes.
2. Calculate the fractional abundance of the second isotope ( ):
Since there are only two isotopes, the sum of their fractional abundances must equal 1.
To subtract, find a common denominator:
3. Calculate the average atomic mass ( ):
The average atomic mass is calculated using the formula:
Substitute the known values:
4. Perform the multiplication:
Calculate the contribution of each isotope:
Contribution of Isotope 1:
Contribution of Isotope 2:
5. Sum the contributions to find the average atomic mass:
6. Round to appropriate significant figures:
The input masses ( and ) have four significant figures. The abundances ( and ) are exact fractions, so the result should be rounded to four significant figures.
The average atomic mass (in amu) of Lz is .