The atomic masses of most elements are fractional because they represent the weighted average of the masses of the naturally occurring isotopes of that element. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons.
The atomic mass of an element takes into account the abundance of each isotope and their respective masses. Since different isotopes of an element can have different masses, the atomic mass is calculated as a weighted average, where the abundance of each isotope is multiplied by its mass and then summed together.
The fractional atomic masses arise due to the relative abundance of different isotopes in nature. Isotopes can have varying abundances, with some being more common than others. The atomic mass calculation considers the percentage or fraction of each isotope present in a natural sample of the element.
For example, carbon has two common isotopes: carbon-12 and carbon-13. Carbon-12 is more abundant in nature, with a relative abundance of about 98.9%, while carbon-13 has a relative abundance of about 1.1%. When calculating the atomic mass of carbon, the masses of carbon-12 and carbon-13 are multiplied by their respective abundances and then summed:
Atomic mass of carbon = (mass of carbon-12 × abundance of carbon-12) + (mass of carbon-13 × abundance of carbon-13)
This calculation results in an atomic mass of approximately 12.01 atomic mass units (amu), which is a fractional value.
Similarly, the atomic masses of other elements are determined by the abundance of their isotopes, and since isotopic abundances are typically expressed as percentages or fractional values, the resulting atomic masses are also fractional.
It's important to note that some elements may have only one stable isotope, in which case their atomic mass is a whole number. Examples include helium-4, lithium-7, and nitrogen-14.