What quantum number determines the energy level of an electron in an atom?

The principal quantum number determines an electron’s principal energy level in an atom.

Written as n, the principal quantum number can take positive integer values such as 1, 2, 3, and 4. It identifies the electron shell and generally indicates how far the electron is from the nucleus and how tightly it is bound. In a hydrogen atom, the energy is given by Eₙ = −13.6 eV/n², so larger n values correspond to higher, less negative energy levels.

The other quantum numbers describe additional properties. The azimuthal quantum number specifies the orbital subshell and shape, the magnetic quantum number specifies orbital orientation, and the spin quantum number describes intrinsic electron spin. These numbers work together to define an electron’s quantum state.

The answer is most exact for hydrogen-like atoms, where energy depends only on n. In atoms with many electrons, electron–electron interactions cause subshells with the same principal quantum number to have different energies. Even there, however, n remains the standard quantum number associated with the main shell or principal energy level.