The atomic weight shown in the periodic table is what we measure based on the isotopic frequencies prevalent on earth. Different celestial bodies can (and do!) have different isotopic frequencies based on the conditions of their formation
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So it's an average of the different isotopes that can be found? That's interesting, I wonder how they work out that average. Do you have to take samples all over the world?
I did a little research and the answer is pretty interesting!
Originally, chemists assigned hydrogen a mass number of 1, and used that assumption to derive the masses of the other elements. Today we definine "1" as being 1/12 of the weight of Carbon-12 (which is very close to the average weight of hydrogen we use today)
As to the relative frequencies, they can be different at different points on earth, this Chemistry SE answer goes into a lot more detail.
If you have never done "stoichiometry" before it may not be obvious but the periodic table average weights are essential for going from "I have x grams of substance" to "I have x number of atoms/molecules of substance" and from there you can use the equation of your target reaction to precisely predict the outcome of a chemical process. If you were doing very high precision chemistry, the differences in isotopic ratio in your sample vs the standard values could introduce an error but I would guess most of the time it is insignificant.
Is is on the basis of isotopic frequency as @[email protected] mentioned in their comment.
Since an element’s isotopes have different atomic masses, scientists may also determine the relative atomic mass—sometimes called the atomic weight—for an element. The relative atomic mass is an average of the atomic masses of all the different isotopes in a sample, with each isotope's contribution to the average determined by how big a fraction of the sample it makes up.
read more here: KhanAcademy
It’s most prevalent