How to Find Average Atomic Mass From the Periodic Table
The decimal number in an element’s box on the periodic table is its average atomic mass, often called its atomic weight. For chlorine, it is about 35.45 atomic mass units (u). The table provides this value directly. You only need to calculate it if you have isotope masses and abundances and want to check how the average was found.
Average atomic mass is a weighted average. Each isotope contributes according to its frequency in a natural sample. More abundant isotopes have a greater effect on the result.
Find the right number on the periodic table
An element’s box usually includes its name or symbol, atomic number, and atomic mass. Table layouts vary, so check the labels when they are shown.
- Atomic number is a whole number that tells you how many protons an atom has.
- Average atomic mass is usually a decimal. It represents the weighted average mass of the element’s isotopes.
Do not use the atomic number as the atomic mass. For example, chlorine’s atomic number is 17, while its average atomic mass is about 35.45 u.
The average is not the mass of a single chlorine atom. Chlorine occurs as a mixture of isotopes: atoms with the same number of protons but different numbers of neutrons. Their masses differ, so the table reports an average for the mixture.
The IUPAC Commission on Isotopic Abundances and Atomic Weights maintains standard atomic-weight values. Some elements have atomic weights shown as intervals because the isotopic composition of natural samples can vary. For those elements, the value depends on the sample. A single table value is a useful reference for general chemistry, but it may not describe every sample exactly.
How the average is calculated
If a problem gives you isotope data, use this formula:
Average atomic mass = sum of (isotope mass × fractional abundance)
Convert each abundance from a percentage to a decimal before multiplying. For example, 69.2% becomes 0.692. Multiply each isotope’s mass by its fractional abundance, then add the products.
The abundances should add to 1 when written as decimals, or to 100% when written as percentages. If they do not, check whether the data have been rounded or whether an isotope is missing.
One worked example: copper
Copper has two naturally occurring isotopes commonly used in introductory examples. Here are their rounded masses and abundances:
| Isotope | Mass | Natural abundance |
|---|---|---|
| Copper-63 | 62.93 u | 69.2% |
| Copper-65 | 64.93 u | 30.8% |
First, convert the percentages to decimals:
- 69.2% = 0.692
- 30.8% = 0.308
Next, multiply each mass by its abundance:
- Copper-63: 62.93 × 0.692 ≈ 43.55
- Copper-65: 64.93 × 0.308 ≈ 20.00
Add the products:
43.55 + 20.00 ≈ 63.55 u
The result is close to copper’s average atomic mass on a periodic table, about 63.55 u. The isotope masses and abundances in this example are rounded, so the calculation may differ slightly from a value printed to more decimal places.
The average is not the simple mean of the two isotope masses. That would give about 63.93 u, as if both isotopes were equally common. Copper-63 is more abundant, so it pulls the weighted average toward its lower mass.
What the table value can and cannot tell you
A periodic table provides the average atomic mass, not the separate masses and abundances needed to reproduce it. If a question asks you to calculate an average from isotope data, use the values supplied in the question or from a reliable reference. The NIST Chemistry WebBook provides chemistry reference data. Specialist sources may also provide isotope information.
A table value cannot tell you the exact isotope mix in a particular sample. Natural isotopic composition can vary, and reference values may differ slightly in their final digits. For most classroom calculations, use the number printed on the periodic table unless the problem gives a more specific value or asks you to work from isotope data.
The number of decimal places depends on the table and the task. Keep the supplied precision during intermediate steps, then round the final answer as requested. Rounding too early can change the result, especially when several values are multiplied and added.
An estimate based on the most abundant isotope’s mass number can sometimes help you check whether a result is plausible. It cannot replace the weighted-average calculation. The mass number is a whole number that counts protons and neutrons; it is not the precise isotope mass or the element’s average atomic mass.
Key Takeaways
- The decimal in an element’s periodic-table box is its average atomic mass, also called its atomic weight.
- The average is weighted by the natural abundance of each isotope.
- To calculate it from isotope data, convert percentages to decimals, multiply each isotope’s mass by its abundance, then add the products.
- Copper’s rounded isotope data give an average of about 63.55 u.
- The atomic number counts protons. It is not the average atomic mass.
- Use the periodic-table value as a general reference. Use isotope-specific data when a calculation requires the separate masses and abundances.
