Nope, their chemical make up changes, changing the total atomic mass.
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It allows for the relative abundances of different isotopes.
The atomic mass of an element is the weighted average of masses of the isotopes of the element, weighted in proportion to their abundance.
The atomic mass of an element is the weighted average of the masses of all the stable isotopes of the element (if it has any), weighted by the natural occurrence levels of the isotopes in the elements as found on earth or in the atmosphere.
The atomic mass is the mass of an atom of that element in AMUs. (Atomic Mass Units)The atomic number, however, is equivalent to the number of protons in an atom of that element.The mass number of an atom is the total number of protons and neutrons in the nucleus of an atom. This is therefore always a whole number. The relative atomic mass of an element is the weighted average of the masses of the isotopes relative to 1/12 of the mass of a carbon-12 atom.It is a weighted average as it takes into account the relative abundances of the different isotopes (atoms of the same element but with different numbers of neutrons) of an element. This number is found in the periodic table.For example chlorine has two isotopes, 35Cl and 37Cl, in the approximate ratio of 3 atoms of 35Cl to 1 atom of 37Cl.The number of protons and neutrons in a 35Cl atom must add up to 35, the mass number. The relative atomic mass of chlorine takes into account both isotopes and is therefore 35.5.
The average atomic mass of an element is the average of the atomic masses of its isotopes (that is a weighted average). You have to take into account the abundance of each isotope when they do your averaging.