The Lyman Series: Ultraviolet Hydrogen Lines
1 · Predict
Electrons dropping all the way down to the ground state (n = 1) emit the Lyman series. Compared to the Balmer series (dropping to n = 2), would you expect Lyman photons to have more or less energy?
- More energy (shorter wavelength) — dropping to the ground state releases a bigger energy gap than dropping to n = 2.
- Less energy than Balmer transitions.
- The same energy as equivalent Balmer transitions.
2 · Set Up
- Open the lyman-alpha preset and press Reset. This preset's default transition is n = 2 → n = 1 (Lyman-alpha).
- Enable the emitted-wavelength readout.
- Set the starting energy level n_initial for each trial (dropping down to n_final = 1) and record the emitted wavelength.
3 · Collect Data
| Starting level n_i | Emitted wavelength λ (nm) |
|---|---|
| 2 | |
| 3 | |
| 4 |
Plot emitted wavelength λ (y-axis) against starting level n_i (x-axis) for your three trials.
4 · Analyze
- For one trial, compute 1/λ = R(1/n_f² − 1/n_i²) using n_f = 1. Compare to the table. Confirm all three wavelengths fall below 122 nm — deep ultraviolet, invisible to the eye.
- Compare your Lyman wavelengths to the balmer-alpha experiment's visible-light wavelengths. Explain why dropping to n = 1 (a much bigger energy gap than dropping to n = 2) always produces higher-energy, shorter-wavelength photons.
5 · Extend
- Lyman-series ultraviolet light is almost entirely absorbed by Earth's atmosphere before reaching the ground. Explain why space telescopes (rather than ground-based ones) are needed to observe hydrogen's Lyman-alpha emission from distant astronomical objects.
- As n_i → ∞, 1/λ approaches R exactly (the series limit), corresponding to an electron barely escaping the atom entirely (ionization) rather than a specific transition. Using your formula, explain why the series limit represents the ionization energy from the ground state.
The Physics Behind This Experiment
Lyman Series (Ground-State Transitions)
Transitions ending at n_f = 1 release the largest possible energy gaps in hydrogen, since the ground state sits far below every excited level — producing the shortest-wavelength (highest-energy) spectral series, entirely in the ultraviolet.