Rydberg Equation
Predict wavelengths of hydrogen spectral lines
Formula
1/λ = RH (1/n₲ - 1/n₂²)
- λ = wavelength (m)
- RH = Rydberg constant (1.097 × 10â· mâ»Â¹)
- nâ‚ = lower energy level
- nâ‚‚ = higher energy level (nâ‚‚ > nâ‚)
Example: Balmer Series (nâ‚ = 2)
Find λ for transition n₂ = 3 → n₠= 2.
1/λ = (1.097 × 10â·) × (1/2² - 1/3²)
1/λ = (1.097 × 10â·) × (1/4 - 1/9) = (1.097 × 10â·) × (5/36)
1/λ ≈ 1.524 × 10ⶠmâ»Â¹
λ ≈ 6.56 × 10â»â· m = 656 nm (red line, Hα)
Answer: λ ≈ 656 nm (visible red)
Spectral Series
Lyman (nâ‚ = 1): UV
Balmer (nâ‚ = 2): Visible
Paschen (nâ‚ = 3): IR
Brackett (nâ‚ = 4): IR
Notes
- Strictly valid for hydrogen; modified for other atoms using Z².
- Energy: ΔE = hc/λ relates wavelength to photon energy.
- n₂ → n₠transition emits photon; reverse absorbs.