The Duality of Time Theory

In 1924, to resolve the inconsistencies between the observed molecular spectra and the predictions of Quantum Mechanics, Wolfgang Pauli (1900-1958) proposed a new quantum degree of freedom, or a quantum number with two possible values. The spectrum of atomic hydrogen had a doublet, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his exclusion principle, stating that “there cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers.” After one year, Pauli’s new degree of freedom was identified with the property of spin, whose effects were observed in the famous Stern-Gerlach experiment.

Schroedinger calculated the energy levels of hydrogen by treating its electron as a wave, represented by the wave-function, in an electric potential well created by the proton. The solutions to Schroedinger’s equation are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model. Schroedinger found that each electron has four properties:

1.An “orbital” designation, indicating whether the particle wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy. 2.The “shape” of the orbital, spherical or otherwise. 3.The “inclination” of the orbital, determining the magnetic moment of the orbital around the z-axis. 4.The “spin” of the electron.

The collective name for these properties is the quantum state of the electron, given by its wave-function, and it can be described by giving a quantum number to each of these properties. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four quantum numbers. This gives rise to different possible arrangements of the orbitals, and how the electrons fill them, which that leads to the organization of the periodic table of chemical elements. Also, the way the atomic orbitals on different atoms combine to form molecular orbitals determines the structure and strength of chemical bonds between atoms.