How quantum numbers describe where electrons are found
Bohr’s model explained the line spectrum of hydrogen, where electrons jump between energy levels and emit light of definite wavelengths given by the Rydberg formula. However, it could not explain atoms with many electrons. The quantum mechanical model uses Heisenberg’s uncertainty principle and de Broglie’s idea of electron waves, describing electrons through orbitals, which are regions of high probability of finding an electron.
Each electron is described by four quantum numbers: the principal quantum number n gives the shell, the azimuthal quantum number l gives the subshell shape (s, p, d, f), the magnetic quantum number m gives the orientation and the spin quantum number gives +½ or −½. Electrons fill orbitals by the Aufbau principle in order of increasing (n + l), follow Pauli’s exclusion principle so no two electrons share all four numbers, and obey Hund’s rule by occupying degenerate orbitals singly first. Chromium and copper are exceptions, with configurations 3d⁵4s¹ and 3d¹⁰4s¹ because half-filled and filled subshells are extra stable.
Why it matters
Spectra let astronomers identify elements in distant stars and chemists analyse samples using spectroscopy. Neon signs, sodium street lamps and lasers all depend on electron transitions. Orbital diagrams explain periodic trends, bonding, magnetism and colour, so this topic underpins almost all of Class 11 and 12 chemistry.
Key terms
- Orbital
- A region around the nucleus where the probability of finding an electron is high.
- Aufbau principle
- Electrons fill orbitals in order of increasing energy.
- Pauli exclusion principle
- No two electrons in an atom can have the same set of four quantum numbers.
- Hund’s rule
- Electrons occupy degenerate orbitals singly with parallel spins before pairing up.