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Is the letter n used to designate the principal quantum number?

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The short answer to your question is yes, the principle quantum number is denoted by a lower case n.  There are four quantum numbers used to describe any given electron in an atom, the principle quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin number.  They are denoted by the symbols, n, l, m, and s.  The principal quantum number, n, denotes the main energy shell of the electron and is represented by a positive integer (1, 2, 3, etc).  The higher the principle quantum number, the higher the energy level of the electron.

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