Quantum-Mechanical Model of the Atom Describes the probability that the electron will be in a certain region of space at a given instant. Orbitals are regions of different energies where the electrons can be found.

The quantum-mechanical model uses 3 quantum numbers to describe an orbital: The principal quantum number (n) Can be any positive integer (n=1, n=2, n=3, etc.) Describes the energy level

The angular momentum quantum number (l) Lowercase cursive L Can have values from 0 to (n–1) Defines the shape of the orbital The magnetic quantum number (ml) Can have integer values between – l and + l Describes the orientation of the orbital in space Value of l 1 2 3 Orbital shape s p d f

# of orbitals in subshell Possible values of l Subshell possible values of ml # of orbitals in subshell Total # of orbitals 1 2 3 4

s orbitals Have a spherical shape. There is one orbital in each s subshell.

p orbitals Dumbbell shaped orbitals Each p subshell contains 3 orbitals. Each of the 3 orbitals is oriented along a different axis (x, y, or z)

d orbitals Each d sublevel contains 5 orbitals. 4 of the 5 orbitals have a four-leaf clover shape. The dz2 orbital has lobes on the z axis and a “doughnut” shape in the x-y plane.

f orbitals An f sublevel will contain 7 orbitals

A maximum of 2 electrons can be located in a given orbital. All orbitals in the same subshell are said to be degenerate, meaning that they have the same energy. (i.e. the 3 orbitals in the 2p sublevel each have the same energy). A maximum of 2 electrons can be located in a given orbital. Type of Sublevel # of orbitals # of electrons s p d f

Subshells Subshell Number of Orbitals Max # of Electrons s 1 2 p 3 6 d 5 10 f 7 14

The fourth quantum number The magnetic spin quantum number (ms) Can have a value of either + ½ or – ½ Represents the electron’s spin about its axis, which can generate a magnetic field in two possible directions. The Pauli Exclusion Principle No two electrons in an atom can have the same quantum numbers. Therefore two electrons found in the same orbital will have opposite spins (+ ½ and – ½)

Rules for writing electron configurations: Aufbau Principle: orbitals are filled in order of increasing energy (lowest energy orbitals filled first). Pauli Exclusion Principle: no more than two electrons can be found in a single orbital. Two electrons in the same orbital have opposite spins. Hund’s Rule: for degenerate orbitals, the lowest energy is obtained when the number of electrons with the same spin is maximized.

outer-shell electrons Valence Electrons outer-shell electrons Include s and p electrons in the highest energy level Electrons that are involved in chemical bonding Core Electrons = inner-shell electrons For example, a phosphorus atom has 15 total electrons Phosphorus has 5 valence electrons (the electrons in the 3s and 3 p orbitals) Phosphorus has 10 core electrons (found in the first and second energy levels)

The octet rule atoms tend to form chemical bonds to reach a full outer-shell of 8 valence electrons. For example, the phosphorus atom on the previous slide would gain three electrons to reach a full outer shell. This P3- ion would have the same electron configuration as the element argon. When an atom and an ion have the same electron configuration, they are said to be isoelectronic.

Transition metal ions d and f electrons are not considered valence electrons. Outer shell s and p electrons will be lost first. For example: Fe Fe2+ Fe3+