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The atomic number is a fundamental characteristic of an element and essentially defines what an element is. It corresponds to the number of protons found in the nucleus of an atom and is denoted by the symbol 'Z'. For example, all carbon atoms have 6 protons; thus, the atomic number of carbon is 6.

This atomic number serves as an identifier because no two elements can have the same number of protons. It means that while looking at the periodic table, the position of each element is determined by its atomic number. Despite the presence of isotopes, the atomic number remains constant and unchanged because isotopes of an element do not differ in the number of protons.

While the atomic number, which is the number of protons, remains the same for all isotopes of a given element, it is the number of neutrons that can vary, giving rise to different isotopes. Neutrons are electrically neutral particles found in the nucleus that contribute significantly to an atom's mass.

For instance, carbon-12 and carbon-14 are both isotopes of carbon, which means they both have 6 protons. However, carbon-12 has 6 neutrons while carbon-14 has 8 neutrons. The variation in neutron count is what makes isotopes of the same element have different atomic masses. This neutron variation is crucial because it can lead to differences in stability and radioactivity among the isotopes.

The mass number, symbolized by 'A', is the total number of protons and neutrons in an atom's nucleus, and it gives the approximate mass of that atom. Since isotopes have a differing number of neutrons, their mass numbers also differ. This is important because the mass number is used to specify individual isotopes and can be used to calculate the relative atomic mass of an element if the abundance of each isotope is known.

Understanding mass number differences is essential for calculations in nuclear chemistry and physics. For instance, mass spectrometry—a technique used to identify different isotopes—relies on differences in mass number to separate isotopes based on their mass-to-charge ratio.