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How is the atomic number of an atom defined?

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The single most important characteristic of an atom is its atomic number (usually denoted by the letter Z), which is defined as the number of units of positive charge (protons) in the nucleus. For example, if an atom has a Z of 6, it is carbon, while a Z of 92 corresponds to uranium.

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When are isotopes stable?

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Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors.
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Isotopes are said to be stable if, when left alone, they show no perceptible tendency to change spontaneously. A uniform scale of nuclear stability that applies to both stable and unstable isotopes alike is based on comparing measured isotope masses with the masses of their constituent electrons, protons, and neutrons.