Rydberg Equation
Predict wavelengths of hydrogen spectral lines
Formula
1/λ = RH (1/n₁² - 1/n₂²)
- λ = wavelength (m)
- RH = Rydberg constant (1.097 × 10⁷ m⁻¹)
- n₁ = lower energy level
- n₂ = higher energy level (n₂ > n₁)
Example: Balmer Series (n₁ = 2)
Find λ for transition n₂ = 3 → n₁ = 2.
1/λ = (1.097 × 10⁷) × (1/2² - 1/3²)
1/λ = (1.097 × 10⁷) × (1/4 - 1/9) = (1.097 × 10⁷) × (5/36)
1/λ ≈ 1.524 × 10⁶ m⁻¹
λ ≈ 6.56 × 10⁻⁷ m = 656 nm (red line, Hα)
Answer: λ ≈ 656 nm (visible red)
Spectral Series
Lyman (n₁ = 1): UV
Balmer (n₁ = 2): Visible
Paschen (n₁ = 3): IR
Brackett (n₁ = 4): IR
Notes
- Strictly valid for hydrogen; modified for other atoms using Z².
- Energy: ΔE = hc/λ relates wavelength to photon energy.
- n₂ → n₁ transition emits photon; reverse absorbs.