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

1. Open the balmer-alpha preset and press Reset. This preset's default transition is n = 3 → n = 2 (Hα, the red Balmer line).
2. Enable the emitted-wavelength readout.
3. Set the starting energy level n_initial for each trial (dropping down to n_final = 2) and record the emitted wavelength.

3 · Collect Data

Plot 1/λ (y-axis) against 1/n_i² (x-axis) for your three trials. Is the line straight?

4 · Analyze

1. For one trial, compute 1/λ = R(1/n_f² − 1/n_i²) using the Rydberg constant R = 1.09678×10⁷ m⁻¹ and n_f = 2. Compare to the table.
2. 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

1. 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.
2. 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

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