Spectral Lines & the Bohr Atom

draft readiness: candidate LightSpectra Both 12 min

Active development: draft / candidate

SoTA UX/pedagogy uplift is complete (playbar transport, deeper challenge deck, tooltip affordances, misconception framing, expanded station snapshots) and regression gates are passing; launch-ready promotion now depends on classroom + screen-reader validation logs.

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Predict

If an electron drops from n = 3 to n = 2 in hydrogen, will the photon be in the UV, visible, or infrared?

Play

Use the core workflow rail: choose context -> set mode -> infer or observe -> explain the pattern.
Set upper level to n = 3 and lower to n = 2 (H-alpha). Note the wavelength and color.
Switch to Inverse mode, enter 656 nm, and solve for the transition; verify it infers Balmer n=3->2.
Increase the upper level: watch the lines converge toward the series limit.
Use the Hydrogen-tab Series Limit Microscope and move n_upper toward infinity to see line pile-up near the Balmer limit.
Switch to Absorption mode: the same wavelengths now appear as dark dips.
Change the series filter to Lyman — these are UV, invisible to our eyes.
Switch to the Elements tab and enable H Balmer comparison to contrast fingerprints against sodium or iron.
Use Mystery Spectrum in the Elements tab, commit to one evidence pattern, then check your answer.
Use the Hydrogen-tab temperature panel to test why Balmer lines peak in A-type stars.

Explain

Use the Bohr energy formula and the Rydberg equation to explain the pattern of spectral lines and why each element has a unique fingerprint.

Learning goals

Explain why atoms emit and absorb light only at specific wavelengths using the Bohr model.
Connect energy-level transitions to the Rydberg formula and predict transition wavelengths.
Distinguish Lyman, Balmer, and Paschen series and identify which fall in visible, UV, and IR bands.
Recognize that each element has a unique spectral fingerprint and explain why.

Misconceptions targeted

Electrons orbit like planets — the Bohr model gives correct energies but not correct spatial pictures.
Emission and absorption lines are unrelated — they occur at the same wavelengths.
All hydrogen lines are visible — only the Balmer series falls primarily in visible light.

Model notes

Hydrogen energy levels computed from the Bohr formula: $E_n = -13.6\ \text{eV} / n^2$ (exact for hydrogen).
For hydrogen, Bohr energies match the exact Schrödinger eigenvalues for the pure $1/r$ Coulomb potential; circular orbits are not physically exact.
Hydrogen tab is model-computed; Elements tab is empirical catalog data (NIST teaching subset), so Bohr ladder semantics apply only to hydrogen.
Bound-state energies are negative because the reference is a free electron-proton pair at infinite separation: $E=0$.
The limit $n=\infty$ is the ionization limit (electron no longer bound), so $E_{\infty}=0$.
As $n_{\text{upper}}$ increases, level spacing shrinks and lines converge toward each series limit.
Emission and absorption use the same $\Delta E$ values and therefore the same wavelengths.
Wavelengths are vacuum wavelengths via $\lambda = hc / \Delta E$ with $hc = 1239.8\ \text{eV·nm}$.
Multi-element line data from the NIST Atomic Spectra Database (strongest lines only).
Mystery mode requires a reflection commitment ('what pattern convinced you?') before reveal to train inference habits.
Temperature readouts use qualitative proxy populations normalized over n=1,2,3 and a Balmer-strength proxy (Boltzmann excitation times neutral-hydrogen proxy), not full radiative transfer.
Bohr atom radii in the visualization use a compressed display scale (labeled 'not to scale').
Line widths in the spectrum strip are for display only (fixed width, not physical broadening).

About this demo

Infer atomic structure from line wavelengths, then invert the task: observed $\lambda$ to inferred transition. The instrument links Bohr structure, series scaling, and stellar-spectrum inference in one loop.