Idiot's Guides - Quantum Physics by Marc Humphrey PhD & Marc Humphrey PhD Paul V. Pancella PhD Nora Berrah PhD & Marc Humphrey PhD Paul V. Pancella PhD Nora Berrah PhD

Author:Marc Humphrey PhD & Marc Humphrey, PhD, Paul V. Pancella, PhD, Nora Berrah, PhD & Marc Humphrey, PhD, Paul V. Pancella, PhD, Nora Berrah, PhD
Language: eng
Format: epub
Publisher: DK Publishing
Published: 2015-01-05T16:00:00+00:00

Revisiting the Periodic Table

Returning to electrons in atoms, the Schroedinger equation still predicts a series of energy levels extending from some lowest level (the ground state) up to the highest energy for which the electron is still bound to the nucleus. The energy levels (Eigenvalues) correspond to quantum states (Eigenfunctions) having different orbital angular momentum values and different orientations. Since the angular momentum doesn’t affect the energy of the state, we have energy degeneracy–multiple states with the same energy. The principle quantum number n is the quantum number that effectively labels the energy of each state.

When we get beyond hydrogen to other elements, each atom now needs more than one electron to make it electrically neutral. (Recall that every different element has certain number of protons in the nucleus, and therefore a different amount of positive charge.) In their most stable state, the sum total energy of all of these electrons is as low as possible. If an electron is in a higher energy level, it spontaneously emits energy (in the form of a photon) as it transitions to a lower energy state.

But the Pauli exclusion principle tells us that if a quantum state is already occupied by an electron, it is impossible for any other electrons to be in the same state. An atom with multiple electrons will naturally fill its lowest energy levels first, additional electrons will fall into states with next higher energies, up until all of its electrons have found a quantum state to occupy.

Since the electron is a spin 1⁄2 particle, it has two possible spin states, up and down. Thus for every state that has the same combination of principle quantum number (n), orbital angular momentum magnitude (l), and orbital angular momentum direction (m), there can be at most two electrons, one with spin up and one with spin down (+1⁄2 and -1⁄2). Each unique state listed in the table at the end of the previous chapter can therefore have zero, one, or two electrons in it.

Pauli’s exclusion principle therefore explains why the periodic table takes the shape that it does. It is all a consequence of filling electron energy levels one by one, from lowest energy on up, with the number of electrons in any state limited by the Pauli principle. In addition, the chemical properties of elements are determined by the quantum state of the outermost electrons, whether the highest energy level is filled or partially filled and what shape it has. (Remember that the shape is determined by the standing wave that satisfies the Schroedinger equation.)