Atomic Orbitals and Electron Arrangement

The Quantum Mechanical Model Erwin Schrodinger Determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus. An atom is modeled as a nucleus surrounded by a fuzzy cloud that represents the probability of finding an electron anywhere within it. Ex. Propellers

Atomic Orbitals The quantum mechanical model was developed from a mathematical equation called the Schrodinger equation. Schrodinger equation = electron’s energy levels = atomic orbital Atomic orbital – a region of space in which there is a high probability of finding an electron.

Atomic Orbitals Energy levels are labeled as principal quantum numbers (n) and are assigned numbers (1, 2, 3, 4, etc.) Energy levels can have different shapes and sublevels. Each energy sublevel corresponds to an orbital of a different shape, which describes where the electron is likely to be found.

Principal Energy Levels and Sublevels The lowest principal energy level has only one sublevel (1s) The second principal energy level has two sublevels (2s and 2p) The third principal energy level has three sublevels (3s, 3p, 3d) The fourth principal energy level has four sublevels (4s, 4p, 4d, 4f)

Maximum Numbers of Electrons Principal quantum number = number of sublevels within principal energy level Formula to determine the maximum number of electrons that can occupy a principal energy level is 2n2.

Electron Arrangement Electrons and the nucleus interact to make the most stable arrangement possible, called electron configurations. 3 rules on how to find electron configurations of atoms: Aufbau principle Pauli exclusion principle Hund’s rule.

Aufbau Principle Electrons occupy orbitals of lowest energy first. Each box represents an atomic orbital.

Pauli Exclusion Principle An orbital can describe at most two electrons. To occupy the same orbital electrons must have opposite spins

Hund’s Rule One electron enters each orbital until all the orbitals contain one electron with the same spin direction.

Exceptions to the Rules Some electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations. For elements up to vanadium (atomic #23) you can use the aufbau diagram for orbital filling. Ex. chromium and copper. Exceptions are due to subtle electron-electron interactions in orbitals with very similar energies.