Spectrum of Neutral Sodium and the D-Line Doublet
1. Electronic Structure of Sodium
- The neutral sodium atom (Na) has 11 electrons.
- 10 electrons are tightly bound in closed inner shells (core electrons).
- These contribute no net angular momentum to the atom.
- The 11th (valence) electron determines the optical properties and spectrum.
2. Principal Series and the D-Line
The D-line doublet (5890 Å and 5896 Å) belongs to the principal series, arising from transitions between:
- Upper state: P-orbital (L = 1)
- Lower state: S-orbital (L = 0)
Fine Structure Terms:
P-state (L = 1): Spin-orbit coupling splits it into two fine-structure levels:
- ²P3/2 (J = 3/2)
- ²P1/2 (J = 1/2)
S-state (L = 0): Only one term:
- ²S1/2 (J = 1/2)
3. Allowed Transitions
The D-line doublet consists of two allowed transitions:
- D₁ line (5896 Å): ²P1/2 → ²S1/2
- D₂ line (5890 Å): ²P3/2 → ²S1/2
Selection Rules:
- ΔL = ±1
- ΔJ = 0, ±1 (but J = 0 → J = 0 is forbidden)
4. Origin of the Doublet
The energy splitting between ²P3/2 and ²P1/2 is due to spin-orbit coupling. This fine-structure splitting explains the two closely spaced D-line wavelengths.