Use our principal quantum number calculator for quick and accurate calculations. Free online tool.
The Principal Quantum Number Calculator computes key properties of electron shells based on the quantum number n (n = 1, 2, 3, ...). The principal quantum number determines the energy level and average distance of an electron from the nucleus, and is the most fundamental of the four quantum numbers in describing atomic structure.
The energy of an electron in hydrogen is given by En = -13.6/n² eV. For n=1, the ground state energy is -13.6 eV; for n=2, it is -3.4 eV; and for n=3, it is -1.51 eV. As n increases, the electron is farther from the nucleus, more loosely bound, and requires less energy to ionize.
Enter n to calculate the electron shell energy, the maximum number of electrons (2n²), the allowed values of l (0 to n-1), and the total number of orbitals (n²). This tool supports chemistry and physics coursework covering hydrogen atom spectra, energy level diagrams, and Bohr model calculations.
The principal quantum number n represents the main energy level or electron shell of an atom; larger n means higher energy and greater distance from the nucleus.
The energy is En = -13.6/n² eV; for example, n=1 gives -13.6 eV (ground state) and n=2 gives -3.4 eV (first excited state).
n takes positive integer values: 1, 2, 3, 4, ... with no upper limit in theory, though in practice electrons beyond n=7 are rarely found in neutral atoms.
Each shell n holds a maximum of 2n² electrons: n=1 holds 2, n=2 holds 8, n=3 holds 18, and n=4 holds 32 electrons.
Shell n contains orbitals with l values from 0 to n-1; for n=3, the available subshells are s (l=0), p (l=1), and d (l=2), totaling n²=9 orbitals.