# Quantum Mechanics

• Orbital: describes a spatial distribution of electron density; an orbital is described by a set of three quantum numbers.

• There is a fourth quantum number called the spin quantum number.

• There are 4 quantum numbers: n, l, ml and ms

• Every electron in an atom has a unique set of quantum numbers

• This set of quantum numbers describes the location of the electron in the atom

• Quantum numbers can be grouped into shells, subshells and orbitals

• Principal quantum number, n: describes the energy level of an electron in an atom; values of n range from n=1 (ground state) to n=infinity (the electron has separated from the atom)

• The values of n can only be integers

• Angular momentum quantum number, l: values are integers from 0 to (n-1); defines the shape of the orbitals

• Letters designate the different values of l

• s=0, p=1, d=2, f=3

• Magnetic quantum number, ml: defines the three-dimensional orientation of the orbital; allowed values of ml are integers ranging from −l to l including 0: −l ≤ ml ≤ l

• Spin quantum number, ms: the “spin” of an electron describes its magnetic field, which affects its energy; the spin quantum number has only two allowed values, +1⁄2 and –1⁄2.

• In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

# s Orbitals

• The value of l for s orbitals is 0.

• They are spherical in shape.

• The radius of the sphere increases with the value of n.

# p Orbitals

• The value of l for p orbitals is 1.

• They have two lobes with a node between them.

# d Orbitals

• The value of l for a d orbital is 2.

• Four of the five d orbitals have four lobes; the other resembles a p orbital with a doughnut around the center.

# f Orbitals

• The value of l for an f orbital is 3

• There are 7 f orbitals

# Energies of Orbitals

• As the number of electrons increases, so does the repulsion between them.

• Therefore, in atoms with more than one electron, not all orbitals on the same energy level are degenerate.

• Orbital sets in the same sublevel are still degenerate.

• Energy levels start to overlap in energy (e.g., 4s is lower in energy than 3d.)

# Electron Configurations

• Electron configuration: the way electrons are distributed in an atom

• Ground state: the most stable organization is the lowest possible energy

• Each electron configuration consists of: a number denoting the energy level; a letter denoting the type of orbital; a superscript denoting the number of electrons in those orbitals.

# Orbital Diagrams

• Each box in the diagram represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the relative spin of the electron.

# Hund’s Rule

• When filling degenerate orbitals the lowest energy is attained when the number of electrons having the same spin is maximized.

• Hund’s rule: for a set of orbitals in the same sublevel, there must be one electron in each orbital before pairing and the electrons have the same spin, as much as possible.

# Pauli Exclusion Principle

• No two electrons in an atom can have the same set

of four quantum numbers n, l, ml and ms

• An orbital can hold a maximum of two electrons and they must have opposite spin.

# Transition Metals

• Transition metals follow the filling of 4s by filling 3d in the 4th period.

# Lanthanides and Actinides

• The elements which fill the f orbitals have special names as a portion of a period, not as a group.

• Lanthanide elements (atomic numbers 57 to 70): have electrons entering the 4f sublevel.

• Actinide elements (including Uranium, at. no. 92, and Plutonium, at. no. 94): have electrons entering the 5f sublevel.

# Periodic Table

• We fill orbitals in increasing order of energy.

• Different blocks on the periodic table correspond to different types of orbitals

• Main-group elements: the s and p blocks