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