Atomic structure: quantum numbers and electron configuration

In 1911 Rutherford showed that an atom has a small, heavy, positively charged nucleus at its centre with electrons moving around it (the planetary model). By this model a circling electron should lose energy and fall into the nucleus; Bohr therefore proposed that the electron’s energy changes only in portions, quanta, and that the electron moves in definite orbits without radiating energy. In the present quantum model the electron has both particle and wave properties: it cannot be placed on a fixed path but only found in an atomic orbital, a region of space where the probability of finding it is about 90 %. The state of an electron is given by four quantum numbers: the principal n (energy level, n = 1, 2, 3 …), the orbital l (orbital shape, l = 0 to n – 1: s, p, d, f), the magnetic mₗ (orientation of the orbital, 2l + 1 values) and the spin mₛ (+½ or –½). By the Pauli principle no two electrons in an atom have all four quantum numbers equal, so one orbital holds at most two electrons (of opposite spin); a level holds at most 2n² electrons and a sublevel 2(2l + 1). Orbitals fill in the order 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p … (Klechkovsky’s rule: first the state with the smaller n + l, and for equal sums the smaller n), and among orbitals of equal energy the electrons first occupy them singly (Hund’s rule).