The Paschen Series: Infrared Hydrogen Lines
1 · Predict
Electrons dropping to n = 3 (the Paschen series) release smaller energy gaps than the Balmer or Lyman series. Does this mean Paschen photons fall in the infrared, beyond what the eye can see?
- Yes — smaller energy gaps mean longer wavelengths, pushing Paschen lines into the infrared.
- No — Paschen lines are still visible.
- Paschen lines are actually higher energy, in the X-ray range.
2 · Set Up
- Open the paschen-beta preset and press Reset. This preset's default transition is n = 5 → n = 3 (Paschen-beta).
- Enable the emitted-wavelength readout.
- Set the starting energy level n_initial for each trial (dropping down to n_final = 3) and record the emitted wavelength.
3 · Collect Data
| Starting level n_i | Emitted wavelength λ (nm) |
|---|---|
| 4 | |
| 5 | |
| 6 |
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 = 3. Compare to the table. Confirm all three wavelengths fall above 1000 nm — infrared.
- Compare the size of these wavelengths to the balmer-alpha and lyman-alpha experiments. Explain the overall pattern: series ending at higher n_f (a smaller energy gap to the ground reference level) produce longer-wavelength, lower-energy photons.
5 · Extend
- Hydrogen's energy levels get closer together as n increases (E_n ∝ −1/n²), so transitions between high levels release less energy than transitions involving low levels. Explain why this crowding of levels at high n explains why the Paschen series (n_f = 3) spans a wider range of energies than you might first expect.
- Infrared astronomy uses exactly these Paschen (and even longer-wavelength Brackett, Pfund) series lines to study hydrogen in dusty regions of space where visible light is blocked. Why might infrared light penetrate cosmic dust better than visible light?
The Physics Behind This Experiment
Paschen Series (Infrared Transitions)
Transitions ending at n_f = 3 involve smaller energy gaps than the Balmer (n_f = 2) or Lyman (n_f = 1) series, since higher-n levels are more closely spaced — producing longer-wavelength, infrared photons.