Quantum Defect Theory & Rydberg Series

Alkali atoms have a single valence electron shielded by core electrons. The Rydberg formula becomes E_n = −R_∞/(n−δ_ℓ)², where δ_ℓ is the quantum defect — a small shift in effective principal quantum number that captures core penetration.

Hydrogen (δ=0)
Alkali atom (δ>0)
Transition energy
Series limit: −13.606 eV (ionization)
Ground state:
First line:
Rydberg formula:
E_n = −13.606/(n−δ)² eV