concepts of Aufbau's Principle, Hund's Rule, and Pauli's Exclusion Principle

Aufbau's Principle

• Explanation: Aufbau's Principle dictates how electrons fill atomic orbitals in an atom.

• Key Points:

  • Electrons occupy orbitals starting from the lowest energy level to the highest.

  • The 1s orbital is filled first, followed by 2s, then 2p, and so on.

  • Each electron is added to the lowest available energy level before moving to higher energy levels.

• Example: When adding electrons to the 2p orbitals, electrons fill the 2p sublevel (e.g., 2px, 2py, 2pz) one at a time, ensuring lower energy levels are filled first.

Hund's Rule

• Explanation: Hund's Rule governs how electrons are placed into degenerate (same energy) orbitals.

• Key Points:

  • Electrons fill degenerate orbitals with parallel spins (arrows pointing in the same direction) before pairing up.

  • Unpaired electrons are more stable than paired electrons due to electron-electron repulsion.

  • Orbitals are filled one electron at a time with parallel spins before any orbitals are doubly occupied.

• Example: In the 2p sublevel, electrons (e.g., 2px, 2py, 2pz) are added one by one with parallel spins before pairing occurs.

Pauli's Exclusion Principle

• Explanation: Pauli's Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers.

• Key Points:

  • The four quantum numbers (n, l, ml, ms) uniquely describe each electron.

    • n (Principal Quantum Number): Describes the energy level.

    • l (Angular Momentum Quantum Number): Describes the shape of the orbital (s, p, d, f).

    • ml (Magnetic Quantum Number): Describes the orientation of the orbital in space.

    • ms (Spin Quantum Number): Describes the spin of the electron (+1/2 or -1/2).

  • Electrons must have different quantum numbers to occupy the same orbital.

• Example: If two electrons are in the same orbital (e.g., 2px), they must have opposite spins (+1/2 and -1/2).

Summary

• Aufbau's Principle: Electrons fill orbitals from low to high energy.

• Hund's Rule: Electrons fill degenerate orbitals singly with parallel spins before pairing.

• Pauli's Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.