Atomic Orbitals, Quantum Numbers and Chemical Properties

Atomic Orbitals, Quantum Numbers and Bonding Properties

Orbital is the region of space around the nucleus in which there is a high probability of finding an electron with a given energy.

Quantum numbers

The quantum numbers describe the allowed states of an electron in an atom:

• Principal quantum number (n): n takes positive integer values (1, 2, 3, ...) and is related to the size and energy of the orbital.
• Azimuthal (orbital) quantum number (l): l takes integer values from 0 to n−1 and is related to the orbital angular momentum and the shape and energy of the orbital.
• Magnetic quantum number (m_l): m_l takes integer values from −l to +l and is related to the orientation of the orbital in space.
• Spin quantum number (m_s): m_s can be +½ or −½ and is related to the intrinsic spin of the electron.

The first three quantum numbers define the orbital; the fourth defines the spin of the electron.

Electron configuration sequence

Electron configuration (example order):

1s² 2s² 2p⁶ 3s² 4s² 3p⁶ 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s² 5f¹⁴ 6d¹⁰ 7p⁶.

Rules for assigning electronic configuration

The electronic configuration of an atom in its ground state is obtained using the following rules:

• Aufbau principle (minimum energy order): The ground-state electronic configuration is obtained by placing electrons in orbitals in order of increasing orbital energy, usually following the Madelung/Aufbau ordering (often represented with the Möller diagram).
• Pauli exclusion principle: No two electrons in the same atom can have four identical quantum numbers. Therefore, at most two electrons may occupy a single orbital, and they must have opposite spins.
• Hund's rule (maximum multiplicity): When several degenerate orbitals are available, electrons occupy different orbitals singly with parallel spins as far as possible before pairing.

Atomic and ionic sizes

Atomic radius: The atomic radius is defined as half the distance between the nuclei of two identical atoms bonded together.

Ionic radius: The ionic radius is the effective radius of an ion. Anions are generally larger than their parent atoms; cations are smaller.

Energetic properties

• Ionization energy: The energy required to remove an electron from a neutral atom in its ground state to form a cation.
• Electron affinity: The energy change (often released) when a neutral atom in its ground state gains an electron to form an anion.
• Electronegativity: The tendency of an atom to attract electrons toward itself in a chemical bond.

Lattice (reticular) energy

Lattice energy (also called reticular energy) is the energy of formation of one mole of an ionic solid from its constituent gaseous ions separated at infinite distance. It is directly proportional to the charges of the anion and cation and inversely proportional to the equilibrium distance between their nuclei, and it depends on constants such as Avogadro's number and the Madelung constant.

Covalence and bonding

Covalence: The number of covalent bonds that an element can form depends mainly on the number of unpaired valence electrons. Examples: H forms 1 bond; O commonly forms 2 bonds.

Resonance structures

Resonance structure: Each resonance structure is one of the Lewis structures that represent a molecule or polyatomic ion and differ only in the distribution of electrons (typically pi electrons or lone pairs).

Dative (coordinate) covalent bond

Dative covalent bond (coordinate bond): A bond formed when one atom provides a pair of electrons (a filled valence orbital) and the other atom provides an empty orbital. Example: formation of NH₄⁺ where one nitrogen lone pair is donated to bond with a proton (H⁺).