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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.
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:
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:
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 (
The input masses (
The average atomic mass (in amu) of Lz is