What does the atomic mass A represent?

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Mass number A counts how many nucleons are in the nucleus, which is the total number of protons and neutrons. In other words, A = Z + N. This is what identifies an isotope, since different isotopes of the same element have the same number of protons (Z) but different numbers of neutrons (N). The number of protons determines the element’s identity and the nuclear charge, while electrons balance that charge in a neutral atom, but neither electrons nor the charge are what A measures. So the mass number specifically reflects the total count of nucleons, protons plus neutrons.