The atomic weight of an element is determined by calculating the weighted average of the masses of its naturally occurring isotopes. Each isotope of an element has a different mass due to variations in the number of neutrons within the nucleus. The abundance of each isotope in a natural sample contributes to the overall atomic weight.
For example, consider the element carbon, which has two stable isotopes: carbon-12 (12C) and carbon-13 (13C). Carbon-12 makes up about 98.9% of natural carbon, while carbon-13 accounts for about 1.1%. To calculate the atomic weight of carbon, we multiply the mass of each isotope by its relative abundance (as a fraction) and then sum these values:
- Atomic weight = (mass of 12C × fraction of 12C) + (mass of 13C × fraction of 13C)
This method provides a more accurate representation of the element’s mass as it reflects the isotopic distribution found in nature. The atomic weight is usually expressed on a scale where carbon-12 is defined as exactly 12 atomic mass units (amu).