Quantum Numbers AP Chemistry: Chapter 7

Aufbau Principle Each electron occupies the lowest energy orbital available. All of one type of orbital on a certain energy level are the same energy (DEGENERATE) Due to penetration effect, s orbitals are lower in energy than p orbitals Electrons in an s orbital spend more time closer to the nucleus, so s orbitals have less energy d orbitals are higher in energy than the s orbital ONE energy level below f orbitals are higher in energy than the s orbital TWO energy levels below

Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 1.

Angular Momentum Quantum Number (l) This quantum number defines the shape of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

Angular Momentum Quantum Number (l) Value of l 1 2 3 Type of orbital s p d f

Magnetic Quantum Number (ml) The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of ml are integers ranging from −l to l: −l ≤ ml ≤ l Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth.

Magnetic Quantum Number (ml) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells. © 2012 Pearson Education, Inc.

Electron Spin Experiments by Stern and Gerlach showed that a beam of silver atoms is split in two by a magnetic field. The experiment reveals that the electrons spin on their axis. As they spin, they generate a magnetic field. Spinning charged particles generates a magnetic field. If there is an even number of electrons, about half the atoms will have a net magnetic field pointing “north” and the other half will have a net magnetic field pointing “south.”

Pauli Exclusion Principle No two electrons in an atom may have the same set of four quantum numbers. Therefore, no orbital may have more than two electrons, and they must have opposite spins.

The Property of Electron Spin Spin is a fundamental property of all electrons. All electrons have the same amount of spin. The orientation of the electron spin is quantized, it can only be in one direction or its opposite. Spin up or spin down The electron’s spin adds a fourth quantum number to the description of electrons in an atom, called the spin quantum number, ms

Spin Quantum Number, ms, and Orbital Diagrams ms can have values of +½ or −½. Orbital diagrams use a square to represent each orbital and a half-arrow to represent each electron in the orbital. By convention, a half-arrow pointing up is used to represent an electron in an orbital with spin up. Spins must cancel in an orbital. Paired

Hund’s Rule The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate (same energy) orbitals. In a set of degenerate orbitals, fill one electron at a time before pairing in same orbital

Allowed Quantum Numbers

Quantum Numbers for the First Four Levels of Orbitals

Orbital Diagram A notation that shows how many electrons an atom has in each of its occupied electron orbitals. Oxygen: 1s22s22p4 Oxygen: 1s 2s 2p

Valence Electrons The electrons in the outermost principal quantum level of an atom. 1s22s22p6 (valence electrons = 8) The elements in the same group on the periodic table have the same valence electron configuration.