Modern Physics

Paschen β line

Infrared Paschen series — longer wavelength emission.

Paschen β line — interactive Modern Physics simulation. Infrared Paschen series — longer wavelength emission. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.

Paschen series

Infrared Paschen series — longer wavelength emission.

The Paschen series (transitions to n = 3) falls in infrared, illustrating how principal quantum number sets photon energy across decades of wavelength. Infrared lines appear in cool hydrogen gas and certain laser transitions.

• IR transition
• n → 3

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

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?

Predictions to weigh

• 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.

Variable roles

What you set:

• Starting level n_i

What you measure:

• Emitted wavelength λ (nm)

How the investigation runs

1. Open the paschen-beta preset and press Reset. This preset's default transition is n = 5 → n = 3 (Paschen-beta).
2. Enable the emitted-wavelength readout.
3. Set the starting energy level n_initial for each trial (dropping down to n_final = 3) and record the emitted wavelength.

Governing equation

Paschen Series (Infrared Transitions) — λ = hc/ΔE

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.

What the printable worksheet asks students to work out

• 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.

Where this shows up beyond the lab

• 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?

• 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

1. Welcome to Paschen Beta
2. Select the atom
3. Press Play
4. Infrared transition
5. Open the Properties panel
6. You did it!

Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.

Open Interactive Lab →

Download lab sheet →

The Bohr Model & Hydrogen Spectra