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Quantum & Atomic Physics

Principal Quantum Number

The primary quantum number designating the main electron shell, overall orbital size, and principal energy level of an electron in an atom.

Governing formula n = 1, 2, 3, 4...
SI unit Dimensionless Integer

In depth

As integer n increases, the electron orbital's mean distance from the nucleus increases and its binding energy decreases. For single-electron hydrogen atoms, energy depends strictly on n (E_n = -13.6 eV / n²).

Examples in the real world

The n=1 shell accommodating a maximum of 2 electrons, while the n=2 shell holds up to 8 electrons (2 n² capacity).