Electronic Configuration & Quantum Numbers

• Electronic configuration refers to the systematic arrangement of electrons within an atom's orbitals.

Electronic Configuration

• It involves organizing electrons from the lowest to the highest energy orbitals.
• It details the arrangement of electrons in shells (K, L, M, N) and sub-shells (s, p, d, f).
• Quantum numbers play a vital role in determining electronic configuration.

Quantum Numbers

• These numbers describe the position and energy of an electron in an atom.
• There are four quantum numbers: principal, azimuthal, magnetic, and spin.

Principal Quantum Number (n)

• Denoted by "n", it describes the energy levels or shells around the nucleus.
• "n" can never be zero, and typically ranges from 1 to 4.

Angular Momentum or Azimuthal Quantum Number (l)

• Denoted by "l", it describes the shape of sub-energy levels within main shells.
• There are four sub-energy levels: s, p, d, and f.
• The relationship between "n" and "l" is given by l ≥ n-1.

Magnetic Quantum Number (ml)

• Denoted by "ml", describes the orbitals within the sub-shells.
• Orbitals occupy the 3-dimensional space around the nucleus where the probability of finding an electron is highest.
• The relationship between "l" and "ml" is given by -l ≤ ml ≥ +l

Electron Spin Quantum Number (ms)

• Denoted by "ms", it describes the motion of an electron within an orbital, having two possible values: +1/2 or -1/2.
• ms = ±1/2.

Aufbau Principle

• Electrons fill orbitals in increasing order of energy levels.
• The lowest energy level fills its maximum number of electrons before the next orbital starts filling.

Pauli's Exclusion Principle

• An orbital can accommodate a max of 2 electrons, but with opposite spins.
• No two electrons in the same atom have the same set of all four quantum numbers.

Hund's Rule

• Pairing of electrons in any orbital happens only after each degenerate sub-orbital has been singly filled with the same spin.
• For p-orbitals with 3 degenerate energy levels, each degenerate orbital is filled with one electron before any pairing occurs (px1, py1, pz1).
• Orbitals of equal energy are referred to as degenerate.

Filling Orbitals

• Atoms of each element vary in the number and energies of their electrons.
• Electrons in an atom have discrete energy levels depending on their distance from the nucleus.
• Orbitals are arranged in order of increasing energy.
• An orbital can hold no more than two electrons.
• Within an energy level, incoming electrons occupy the lowest energy orbitals first (e.g., 4s fills before 3d).
• At each energy level, orbitals are singly filled in one direction before electron pairing.

Electronic Configuration Examples

• Filled sub-shells, whether singly or doubly filled, are stable and may not easily lose electrons.
• The configuration with the lowest electronic energy is called the ground state; other configurations are excited states.

Shapes of Orbitals

• Orbitals are the space around the nucleus with a high probability of finding electrons.