The Balmer Series: Visible Hydrogen Spectral Lines
1 · Predict
An electron in a hydrogen atom drops from a higher energy level down to level n = 2, emitting a photon (the Balmer series — the only hydrogen lines visible to the human eye). Does the emitted wavelength depend on which level the electron started from?
- Yes — different starting levels give different, discretely-spaced wavelengths (the Balmer lines Hα, Hβ, Hγ...).
- No — every transition down to n = 2 emits the same wavelength.
- The wavelength can be anything in a continuous range, not discrete values.
2 · Set Up
- Open the balmer-alpha preset and press Reset. This preset's default transition is n = 3 → n = 2 (Hα, the red Balmer line).
- Enable the emitted-wavelength readout.
- Set the starting energy level n_initial for each trial (dropping down to n_final = 2) and record the emitted wavelength.
3 · Collect Data
| Starting level n_i | Emitted wavelength λ (nm) |
|---|---|
| 3 | |
| 4 | |
| 5 |
Plot 1/λ (y-axis) against 1/n_i² (x-axis) for your three trials. Is the line straight?
4 · Analyze
- For one trial, compute 1/λ = R(1/n_f² − 1/n_i²) using the Rydberg constant R = 1.097×10⁷ m⁻¹ and n_f = 2. Compare to the table.
- Explain why the wavelengths get shorter (higher energy) as n_i increases, but the spacing between successive lines (Hα, Hβ, Hγ) shrinks — they converge toward a series limit rather than spreading apart indefinitely.
5 · Extend
- The Balmer series is the only hydrogen series that falls in the visible spectrum (roughly 400–700 nm) — that's why it's the one historically discovered first, by Johann Balmer in 1885, before the underlying atomic theory existed. Explain why the Lyman series (dropping to n = 1) and Paschen series (dropping to n = 3) fall outside visible light.
- Astronomers identify hydrogen in distant stars by detecting these exact Balmer wavelengths in starlight spectra. Explain why finding a shifted (not exact) Balmer-alpha wavelength in a star's spectrum tells astronomers the star is moving relative to Earth (the Doppler effect).
The Physics Behind This Experiment
Rydberg Formula (Bohr Model)
The wavelength of light emitted when a hydrogen electron drops from level n_i to n_f follows 1/λ = R(1/n_f² − 1/n_i²), where R is the Rydberg constant — a direct consequence of the Bohr model's quantized energy levels.