26.3 Wave Functions and Atomic Orbitals | General Physics

Chad provides a detailed lesson on Wavefunctions and Atomic Orbitals. Chad begins by describing that electrons do not occupy circular orbits as described by the Bohr model of the atom, but actually atomic orbitals. These atomic orbitals are regions of space with quantized energies that are representative of wave functions which are derived as solutions to the Schroedinger equation. The fact that the behavior of electrons can be described by these wave functions is a testimony to the proposition by de Broglie that matter also exhibits wave-like behavior. The shapes of common s, p, and d orbitals are depicted.

Next, the Heisenberg Uncertainty Principle is presented which puts fundamental limits on how precisely a particle's position and momentum can be known. Ultimately, the Heisenberg Uncertainty Principle states that the product of the uncertainties of a particle's position and momentum will be greater than or equal to Planck's constant divided by 4 pi. Although less commonly stated as such, it can also be viewed as stating that the product of the uncertainty in a particle's energy and the duration of time is will be greater than or equal to Planck's constant divided by 4 pi.

Next, the energies of the atomic orbitals are presented in an orbital diagram. Atomic orbitals can have a maximum of two electrons. Electrons will generally occupy the lowest energy orbitals before occupying higher energy orbitals. An orbital diagram shows the increasing energy of the various shells and subshells of atomic orbitals making it straightforward to determine which orbitals are occupied by electrons for a given atom.

The four quantum numbers, n, l, ml, and ms, are also introduced and indicate the orbital an electron occupies as well as its spin. n, l, and ml are all derived as part of the solutions of the Schroedinger equation. n is the principle quantum number and indicates the electron shell. l is the orbital or azimuthal quantum number and indicates the electron subshell (s, p, d, f, etc). Ml is the magnetic quantum number and indicates a specific orbital in a subshell which differs in their 3D orientation in space. Finally, Pauli proposed a fourth quantum number, ms--the spin quantum number, which is a reflection of a fundamental property of electrons. There are two types of spin possible which result in opposite interactions with a magnetic field. Pauli also proposed in his Pauli Exclusion Principle that no two electrons can have the same set of four quantum numbers which ultimately means that two electrons in the same orbital must have opposite spins. The lesson is concluded by showing how the filling of electrons in an orbital diagram can be written in a shortened notation called the electron configuration.

00:00 Lesson Introduction
01:02 Wave Functions
06:51 Heisenberg Uncertainty Principle
10:12 Atomic Orbitals and Atomic Orbital Diagram
14:30 Quantum Numbers and the Pauli Exclusion Principle
22:09 Electron Configuration

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