Hydrogen Spectrum - Lyman Series
Example 12.6: Using the Rydberg formula, calculate the wavelengths of the first four spectral lines in the Lyman series of the hydrogen spectrum.
Energy Levels (eV)
n=1: -13.6 eV
n=2: -3.4 eV
n=3: -1.51 eV
n=4: -0.85 eV
n=5: -0.54 eV
Rydberg Formula
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \]
Where \( R_H \) = 1.097×10⁷ m⁻¹
Solution:
For Lyman series (\( n_f = 1 \)):
\[ \lambda_{i1} = \frac{913.4 \, n_i^2}{(n_i^2 - 1)} \, \text{Å} \]
Calculated wavelengths:
| Transition | Wavelength (Å) | Energy (eV) |
|---|---|---|
| 2 → 1 | 1218 | 10.20 |
| 3 → 1 | 1028 | 12.09 |
| 4 → 1 | 974.3 | 12.75 |
| 5 → 1 | 951.4 | 13.06 |
The Lyman series appears in the ultraviolet region of the electromagnetic spectrum.
As the principal quantum number increases, the wavelengths converge toward the series limit at 912 Å.
