Atomic Structure and the Exclusion Principle

Experiments on the photoelectric effect, alongside the infamous double-slit experiment, tell us that light exhibits properties of both particles and waves. Likewise, experiments on electron diffraction tell us that wave-particle duality is a property of fundamental particles such as electrons, as well as of light. The de Broglie relation summarises the relationship between the classical and wave-like properties of matter, giving a link between the classical momentum of a particle and its wavelength:

**de Broglie relation p = h/lambda**

In quantum mechanics, electrons are described by wavefunctions which contain all the necessary information to make predictions about future states of the particle (although Heisenberg's uncertainty principle outlines intrinsic limitations on the predictions we are able to make). These wavefunctions are solutions to the Schrödinger equation; they are analogous to the solutions of the classical wave equation for transverse waves on a string, which also contain all the information needed to make predictions about the shape of the string at future times.  

When electrons exist in bound states they surround the nuclei of their parent atoms, with each electron existing in a quantum state determined by four quantum numbers:

     the principal quantum number, n             (where n ≥ 1)

     the orbital quantum number, l                 (where |l | ≤ n – 1)

     the magnetic quantum number, m_l          (where – l ≤ m_l ≤ l )

     and the spin number, m_s                        (where m_s = ± ½)

The Pauli exclusion principle prohibits more than one electron from occupying a particular quantum state. That is, no two electrons can exist in a state with all four quantum numbers the same. This principle helps us to understand the electron configurations and resulting chemical properties of elements in the periodic table:

     electrons are arranged in shells or orbitals, identified by the principal quantum number n;

     each shell contains subshells, identified by the orbital quantum numbers |l|≤ n – 1;

     within each subshell there exist 2l + 1 states corresponding to different values of the magnetic quantum number m_l

     for each value of m_l there are two electron spin states, either spin +1/2 or -1/2.