The atomic weight of an element is a weighted average of the masses of its naturally occurring isotopes. Isotopes are variants of an element that have the same number of protons but different numbers of neutrons in their nuclei. Since isotopes have different masses, the atomic weight of an element is expressed as a weighted average.
In some cases, an element may have isotopes with significantly different abundances. This can lead to atomic weights that appear as fractions. Let's take the example of chlorine (Cl).
Chlorine has two stable isotopes: chlorine-35 (^35Cl) and chlorine-37 (^37Cl). The atomic weight of chlorine is approximately 35.45. This value is not a whole number because the two isotopes exist in different proportions in nature.
The isotope chlorine-35 is more abundant, making up about 75.77% of naturally occurring chlorine atoms. Chlorine-37 is less abundant, constituting about 24.23% of the atoms. When calculating the atomic weight, the relative abundance of each isotope is taken into account.
The atomic weight calculation for chlorine would be as follows:
Atomic weight = (isotope 1 mass × isotope 1 abundance) + (isotope 2 mass × isotope 2 abundance)
= (35 amu × 0.7577) + (37 amu × 0.2423)
= 26.5245 amu + 8.9641 amu
= 35.4886 amu
This value is rounded to 35.45 amu, which is the atomic weight of chlorine.
So, the fraction in the atomic weight arises due to the different abundances of the isotopes and the weighted average calculation used to determine the overall atomic weight of an element.