how to calculate natural abundance

To calculate the natural abundance (percent abundance) of isotopes of an element, you use the weighted average atomic mass formula based on the isotopic masses and their relative abundances. The steps are as follows:

How to Calculate Natural Abundance of Isotopes

1. Identify the known values:
   • The average atomic mass of the element (from the periodic table).
   • The atomic masses of the individual isotopes.
   • The unknown relative abundances (percentages) of the isotopes.
2. Set variables for the abundances:
   • Let xxx be the abundance (as a decimal or fraction) of one isotope.
   • Then 1−x1-x1−x is the abundance of the other isotope (assuming two isotopes).
3. Write the weighted average mass equation:

Average atomic mass=(M1×x)+(M2×(1−x))\text{Average atomic mass}=(M_1\times x)+(M_2\times (1-x))Average atomic mass=(M1​×x)+(M2​×(1−x))

Where:

• M1M_1M1​ = mass of isotope 1
• M2M_2M2​ = mass of isotope 2
• xxx = fractional abundance of isotope 1

4. Solve for xxx:
   Rearrange the equation to isolate xxx and solve.

5. Convert xxx to percentage:
   Multiply by 100 to get the percent abundance.

Example:

If bromine has isotopes with masses 78.918 u and 80.90 u, and the average atomic mass is 79.9 u, then:

79.9=78.918x+80.90(1−x)79.9=78.918x+80.90(1-x)79.9=78.918x+80.90(1−x)

Solve for xxx to find the percent abundance of bromine-79, then calculate 1−x1-x1−x for bromine-81

Formula for Natural Abundance Calculation

For each isotope:

Natural Abundance (atomic mass units)=Isotopic Mass×(Isotopic Abundance (%)100)\text{Natural Abundance (atomic mass units)}=\text{Isotopic Mass}\times \left(\frac{\text{Isotopic Abundance (%)}}{100}\right)Natural Abundance (atomic mass units)=Isotopic Mass×(100Isotopic Abundance (%)​)

Sum these values for all isotopes to get the average atomic mass

Summary

• Use the average atomic mass as a weighted average of isotope masses.
• Set up an equation with isotope masses and their unknown abundances.
• Solve for the unknown abundance(s).
• Convert decimal abundances to percentages.

This method applies primarily when there are two isotopes but can be extended to more isotopes by adding terms for each isotope's mass times its abundance fraction