Electron Configuration and Orbital Diagrams

Aufbau Principle

  • Definition: Fill electrons from the lowest energy level up to the highest; you must completely fill an energy level before moving to the next.
  • Analogy used in class: video game leveling. Start at level 1 (1s), complete all missions to gain XP, then level up to the next level (2s, then 2p, then 3s, 3p, 4s, etc.).
  • Energy level order mentioned: 1s → 2s → 2p (px, py, pz) → 3s → 3p → 4s → 3d → … (in practice, 3d follows after 4s).
  • Orbitals and capacity:
    • Each orbital can hold up to 2 electrons.
    • Electrons are represented by arrows (up and down) to indicate spin.
  • Notation examples:
    • 1s, 2s, 2px, 2py, 2p_z, 3s, 3p, 4s, 3d, etc.
    • 3d orbitals: five orientations (degenerate in energy within a subshell): d{xy}, d{xz}, d{yz}, d{x^2-y^2}, d_{z^2}.

Orbital capacities and degeneracy

  • p subshell has 3 degenerate orbitals: 2px, 2py, 2p_z.
  • d subshell has 5 degenerate orbitals: d{xy}, d{xz}, d{yz}, d{x^2-y^2}, d_{z^2}.

Electron Spin and Pauli Exclusion Principle

  • Pauli Exclusion Principle: no two electrons in the same atom can have the same set of quantum numbers; in practice, two electrons in a single orbital must have opposite spins.
  • Representation: an orbital can hold two electrons with opposite spins, shown as one ↑ and one ↓.
  • Important nuance from the lesson: you cannot have two electrons both spinning up in the same orbital (that would violate the Pauli principle).
  • Ordering note: which orbital gets the paired electron is not fixed; as long as the pair exists in one orbital and the others are singly occupied when applicable, the arrangement is valid.

Hund's Rule (Hunt's rule in the lecture)

  • Hund's Rule: within a subshell, electrons fill degenerate orbitals singly as far as possible before pairing.
  • Rationale: electrons repel each other, so they prefer to occupy different orbitals to maximize separation (minimize repulsion).
  • Example in a p subshell:
    • With two electrons, you cannot place both in the same p orbital; you place them in two different orbitals (e.g., px and py) with parallel spins.
    • Only after each degenerate orbital contains one electron do you start pairing (add a second electron) in any of the same orbitals.
  • After electrons are paired, they must still obey Pauli exclusion (opposite spins in the same orbital).

Oxygen atom example: orbital diagram and electron configuration

  • Oxygen (O) has atomic number 8, so the electron configuration is:
    1s^2\ 2s^2\ 2p^4
  • Orbital diagram representation:
    • 1s: ↑↓
    • 2s: ↑↓
    • 2p: three degenerate orbitals (px, py, pz)
    • According to Hund's rule, first place one electron in each of the three 2p orbitals with parallel spins: px: ↑, py: ↑, pz: ↑
    • The fourth electron pairs in one of the 2p orbitals (e.g., in px: ↑↓)
  • A concrete arrangement (one valid depiction):
    • 2p: px: ↑↓, py: ↑, pz: ↑
  • This matches the total of eight electrons: 2 (1s) + 2 (2s) + 4 (2p) = 8.
  • Note: The lecture mentioned counting 1, 2, 3, then pairing the second one for the p subshell; the essential idea is the same: fill singly first, then pair.

Ions and orbital diagrams

  • For ions, you add (or remove) electrons following the same filling order, keeping the same rules (Aufbau, Pauli, Hund).
  • The instructor mentioned you can draw the ion’s orbital diagram by adding the appropriate number of electrons to the existing diagram (e.g., adding two electrons to form a -2 ion).

Summary of key rules and conventions

  • Aufbau Principle: fill from the lowest energy level upward; fully fill an energy level before starting the next.

  • Each orbital holds up to exactly two electrons with opposite spins: represented as ↑↓.

  • Pauli Exclusion Principle: no two electrons in an atom can have the same set of quantum numbers; in practice, no two electrons in the same orbital can have the same spin.

  • Hund's Rule: within a subshell, electrons occupy different orbitals first with parallel spins; only after all have one electron do you pair them.

  • Subshell degeneracy and naming:

    • s: 1 orbital
    • p: 3 orbitals (px, py, pz)
    • d: 5 orbitals (d{xy}, d{xz}, d{yz}, d{x^2-y^2}, d_{z^2})

  • Energy-level ordering (as described): 1s < 2s < 2p < 3s < 3p < 4s < 3d

  • Practical example: oxygen configuration is 1s^2\ 2s^2\ 2p^4 with 2p having three singly occupied orbitals and one paired after the fourth electron.

Practice and resources

  • Practice time is reserved for students to work on orbital diagrams and electron configurations.
  • Worksheets on orbital diagrams are available in Schoology.
  • The instructor mentioned you can use signs to complete a project and that printed paper versions (white sheets) are available if needed.

Quick reference formulas and identifiers

  • Maximum electrons per orbital: 2
  • Number of p orbitals: 3
  • Number of d orbitals: 5
  • Electron configuration example: 1s^2\ 2s^2\ 2p^4
  • General energy-order snippet to remember: 1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d$$ (with the practical note that 3d often lies after 4s in many cases)

Physical and practical implications (context from notes)

  • These principles explain how electrons fill into atoms, which in turn determines chemical properties and behavior of elements.
  • The visualization with arrows helps in understanding magnetic properties and spin configurations.
  • Real-world relevance: electron configurations influence bonding, reactivity, and spectroscopic behavior.