Modern Physics
Balmer α (Hα) line
Set n_i→n_f — the emission line colour matches λ from the Rydberg formula.
Observe the Balmer-alpha hydrogen emission line from an atomic electron transition. Explore the Bohr model and discrete atomic spectra.
Balmer series
Set n_i→n_f — the emission line colour matches λ from the Rydberg formula.
Hydrogen transitions to n = 2 emit visible Balmer lines with wavelengths from the Rydberg formula 1/λ = R_H(1/4 − 1/n²). Hα at 656 nm is the brightest red line—used in astronomy to identify hydrogen and measure redshift.
- 1/λ = R(1/2²−1/n²)
- Hα red line
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Starting level n_i
What you measure:
- Emitted wavelength λ (nm)
How the investigation runs
- 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.
Governing equation
Photon Wavelength–Energy Relation — λ = hc/ΔE
Once the Bohr model's energy-level transition (n_i to n_f) gives the emitted photon's energy ΔE, its wavelength follows directly from λ = hc/ΔE — the same relation that links any photon's energy to its wavelength. The level spacing itself, and thus ΔE, is set by the Rydberg formula 1/λ = R(1/n_f² − 1/n_i²).
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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).
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — E.1 Structure of the atom
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Balmer Alpha
- Select the atom
- Press Play
- Visible hydrogen line
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
The Bohr Model & Hydrogen Spectra