Quantum numbers, Aufbau principle, Pauli exclusion principle, Hund’s rule

Quantum Numbers

1. Quantum numbers describe the state and position of an electron in an atom.
2. There are four quantum numbers:
   • Principal Quantum Number (n): Indicates the main energy level or shell of the electron.
   • Azimuthal Quantum Number (l): Defines the subshell and shape of the orbital (0 for s, 1 for p, 2 for d, 3 for f).
   • Magnetic Quantum Number (m_l): Specifies the orientation of the orbital in space.
   • Spin Quantum Number (m_s): Describes the spin of the electron (+1/2 or -1/2).
3. Each electron in an atom is uniquely identified by a set of four quantum numbers.
4. The values of quantum numbers are interdependent, restricting the possible states of an electron.

Aufbau Principle

1. The Aufbau Principle states that electrons occupy the lowest energy orbitals first.
2. Orbital filling follows the order determined by the (n + l) rule, where n is the principal quantum number and l is the azimuthal quantum number.
3. If two orbitals have the same (n + l) value, the orbital with the lower n value is filled first.
4. The order of filling is: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s, and so on.
5. Represents a systematic way to determine the ground-state electron configuration of an atom.
6. Exceptions to the Aufbau principle occur in elements like chromium and copper due to increased stability of half-filled and fully filled orbitals.

Pauli Exclusion Principle

1. Proposed by Wolfgang Pauli in 1925.
2. States that no two electrons in an atom can have the same set of quantum numbers.
3. Ensures that each orbital can hold a maximum of two electrons with opposite spins.
4. Explains the unique electronic structure of each element.
5. Fundamental to understanding the periodic table and chemical properties.

Hund's Rule

1. Proposed by Friedrich Hund in 1927.
2. States that electrons occupy degenerate orbitals (orbitals with the same energy) singly before pairing up.
3. Minimizes electron-electron repulsion by maximizing the number of parallel spins.
4. Ensures the stability of an atom by reducing repulsion in partially filled orbitals.
5. Helps determine the correct electronic configuration of elements, particularly in p, d, and f orbitals.

Electronic Configuration

1. Describes the arrangement of electrons in the orbitals of an atom.
2. Follows the rules of Aufbau principle, Pauli exclusion principle, and Hund's rule.
3. Represented in terms of subshells, e.g., 1s² 2s² 2p⁶.
4. Explains the chemical behavior and reactivity of elements.
5. Helps predict the valency, bond formation, and magnetic properties of elements.
6. Examples:
   • Hydrogen: 1s¹
   • Oxygen: 1s² 2s² 2p⁴
   • Iron: [Ar] 3d⁶ 4s²

Key Points

1. Quantum numbers provide a complete description of an electron's position and energy.
2. Aufbau principle explains the order of orbital filling, while Pauli exclusion principle defines the maximum number of electrons in an orbital.
3. Hund's rule ensures that electrons occupy degenerate orbitals to minimize repulsion.
4. Exceptions to these rules occur due to stability factors in specific elements.
5. Understanding electronic configuration is key to grasping the periodic table and periodic trends.