In quantum physics, which quantum number primarily specifies an electron shell in an atom?

The principal quantum number primarily specifies an electron shell in an atom.

Usually written as n, the principal quantum number takes positive integer values such as 1, 2, and 3. In a hydrogen atom, it determines the electron’s allowed energy level and is also associated with the shell’s overall size. Higher n values generally correspond to higher energy and a larger average distance from the nucleus.

For hydrogen-like atoms, the energy depends directly on n. In multi-electron atoms, electron–electron interactions and shielding mean that energy also depends on other quantum numbers, so shells and subshells are not perfectly described by n alone.

The principal quantum number should not be confused with the azimuthal quantum number, which describes orbital angular momentum and subshell shape, or the magnetic quantum number, which specifies an orbital’s orientation. The spin quantum number describes intrinsic electron spin.