Electron Structure & Light
Quantum numbers, orbital filling, electron configurations, and the light/energy relationships.
Quantum numbers
CORE RULEn = 1, 2, 3, … . For each n, ℓ = 0 to n−1. For each ℓ, mₗ = −ℓ to +ℓ in integer steps. mₛ = +½ or −½.
Subshell codes
REFERENCE| ℓ | Letter | Max e⁻ |
|---|---|---|
| 0 | s | 2 |
| 1 | p | 6 |
| 2 | d | 10 |
| 3 | f | 14 |
Electrons per subshell
CORE RULEA subshell holds 2(2ℓ+1) electrons: s = 2, p = 6, d = 10, f = 14.
Pauli exclusion
CORE RULENo two electrons in an atom share all four quantum numbers. One orbital (n, ℓ, mₗ) holds at most 2 electrons, with opposite spins.
Aufbau fill order
CORE RULEFill by increasing energy: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p.
Hund's rule
CORE RULEWithin a degenerate subshell, place one electron in each orbital (parallel spins) before pairing. Maximum-multiplicity ground state is most stable.
Cr & Cu exceptions
WATCH OUTCr = [Ar] 4s¹ 3d⁵ and Cu = [Ar] 4s¹ 3d¹⁰ (also Mo, Ag, Au): half-filled d⁵ and filled d¹⁰ stability beats the naive Aufbau prediction.
Ion configurations
CORE RULECations lose the highest-n (ns) electrons first, before (n−1)d: Fe [Ar] 4s² 3d⁶ → Fe³⁺ [Ar] 3d⁵.
Anions add electrons in Aufbau order to the next noble gas: O [He] 2s² 2p⁴ + 2e⁻ → O²⁻ [Ne].
Photon energy
CORE RULEE = hν and c = λν, so E = hc/λ. h = 6.626 × 10⁻³⁴ J·s, c = 2.998 × 10⁸ m/s. Higher frequency = shorter wavelength = higher energy.
Bohr energies & transitions
CORE RULEHydrogen-like orbital energy: Eₙ = −2.179 × 10⁻¹⁸ J · Z² / n² (Z = 1 for H).
Transition: ΔE = E_f − E_i (emit if < 0, absorb if > 0). Photon wavelength λ = hc / |ΔE|.
de Broglie wavelength
CORE RULEλ = h / (m·v) = h/p, for a particle of mass m and velocity v. Use SI units (kg, m/s, J·s); λ comes out in metres. Larger momentum (m·v) gives a shorter wavelength.