Electron Orbitals Quantum Numbers Energy Level Diagrams

Quantum Numbers Bohr’s model of the atom did not correctly predict the correct spectral lines for elements other than hydrogen. Further observations revealed that electron orbitals are more complex in higher stationary states.

Quantum Numbers Following Bohr’s contributions, other scientists further improved the electron structure of atoms. Each electron in an atom is described using four different quantum numbers. Each number describes one aspect of the orbital.

Principal Quantum Number n The principal quantum number describes the energy level an electron is found in. This describes how far the electron is from the nucleus of the atom. Therefore, this also describes how large the orbital will be.

Principal Quantum Number n E, Energy

Secondary Quantum Number l Close examination of certain spectral lines reveals they are actually made up of 2 or more distinct lines. This indicates that some shells are actually composed of multiple mini- shells, or subshells. Arnold Sommerfeld theorized that each sub-level has a different elliptical shape.

Secondary Quantum Number l The Secondary Quantum Number, l, represents the sub- levels possible for each shell. The number of different subshells possible is equal to the principal quantum number minus one (n – 1).

Secondary Quantum Number l The values for the Secondary quantum number have names, but are referred to by the first letter of their name. 0 = Sharp 1 = Principal 2 = Diffuse 3 = Fundamental

Magnetic Quantum Number m l In 1897, Peter Zeeman noticed that if a strong magnetic field is present, some spectral lines split into multiple bright lines Arnold Sommerfeld theorized that electron orbitals can be oriented in different directions. The magnetic field therefore affects each orbital differently.

Magnetic Quantum Number m l The Magnetic Quantum Number, m l, refers to the orientation of an electron orbital around the atom. The number of orientations possible is dependent on the secondary quantum number. m l = all possible integers from -l to +l Example, if l = 1, then m l = -1, 0, +1

Spin Quantum Number m s The fourth quantum number is called the Spin Quantum Number, m s. Each electron orbital can hold 2 electrons Each electron is opposite in spin Mathematically this is represented by using half-integers, or +1/2 and -1/2.

Quantum Numbers Create a table to summarize the 4 quantum numbers. Include: Name Symbol What it describes Possible values up to n = 4.

nlmlml msms 100-1/2, +1/ , 0, +1 -1/2, +1/ , 0, +1 -2, -1, 0, +1, +2 -1/2, +1/ , 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 -1/2, +1/2

Energy Level Diagrams Now when we draw energy level diagrams, we must include: the sublevels of each shell orientations for each orbital the spin of each electron

Energy Level Diagrams When creating energy level diagrams for elements, there are two important rules we must obey: Pauli’s Exclusion Principle No two electrons may have the same set of quantum numbers. Hund’s Rule One electron must occupy each orbital of the same energy level before a second electron occupies an orbital.

Energy Level Diagrams When adding electrons in electron configurations, we can use the Aufbau principle to help us (aufbau = “building up”)

Energy Level Diagrams Rules for Anions Add the extra electrons corresponding to the ion charge to the total number of electrons before distributing electrons in orbitals. Rules for Cations Create the energy-level diagram for the neutral atom first, then remove the number of electrons equivalent to the charge from the orbital with the highest principle quantum number first.