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Instructor notes: Spectral Lines & the Bohr Atom

Public notes (v0.2 policy). Not linked from primary navigation.

Exhibit: /cosmic-playground/exhibits/spectral-lines/

Overview

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This guide is instructor-facing Student demo: /play/spectral-lines/
Main code: apps/demos/src/demos/spectral-lines/main.ts
UI logic: apps/demos/src/demos/spectral-lines/logic.ts
Physics model: packages/physics/src/spectralLineModel.ts

Why this demo exists

This demo links three synchronized representations of one physical process:

  • Bohr orbit transitions,
  • quantized energy levels in eV,
  • observed spectral lines in wavelength space.

The instructional target is to move students from memorizing named lines (H-alpha, Lyman-alpha) to using model structure: $E_n = -13.6\ \text{eV}/n^2$ and $E_\gamma = hc/\lambda$.

Learning goals

  • Explain why hydrogen emits/absorbs only specific wavelengths.
  • Predict how line wavelength changes as $n_{\rm upper}$ increases within a fixed series.
  • Distinguish emission vs absorption as the same transition energies with different background conditions.
  • Use line-pattern matching language to motivate element fingerprinting.
  1. Start at Balmer H-alpha ($3\to2$), ask for color prediction before reveal.
  2. Step to H-beta and H-gamma, ask what trend they notice in $\lambda$.
  3. Switch to Lyman and ask why the lines are not visible.
  4. Toggle to Absorption and ask what changed and what did not.
  5. Move to Elements tab for quick “fingerprint” pattern comparison.

Common misconceptions to target

  • “Bohr is totally wrong.”
    For hydrogen energy levels, Bohr energies are correct; the spatial orbit picture is the approximation.

  • “Emission and absorption are different lines.”
    The wavelengths are the same; only bright-vs-dark presentation changes.

  • “Any near-match photon can be absorbed.”
    Bound-bound absorption requires the correct transition energy.

Activities

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MW Quick (4-6 min)

Goal: establish “discrete lines = discrete energy differences.”

  1. Set H-alpha ($n=3\to2$), ask students to predict visible/UV/IR.
  2. Record $\lambda$ and $E_\gamma$.
  3. Step to H-beta ($4\to2$), ask which quantity changes more and why.
  4. Debrief with $E_\gamma = hc/\lambda$.

MW Short (8-12 min)

Goal: series structure + convergence.

  1. Keep Balmer filter active.
  2. Students collect H-alpha, H-beta, H-gamma, H-delta.
  3. Prompt: “What happens to spacing as $n_{\rm upper}$ increases?”
  4. Connect trend to series limit language.

Friday Lab (20-30 min)

Goal: Observable -> Model -> Inference.

  1. Team A: emission run; Team B: absorption run.
  2. Each team gathers a 4-row table (transition, $\lambda$, $E_\gamma$, series).
  3. Swap tables and verify whether the same transitions appear.
  4. Move to Elements tab and attempt one fingerprint match using pattern evidence.

Station version (8-10 min)

Use apps/site/src/content/stations/spectral-lines.md as the printable student artifact.

Assessment

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Clicker prompts

  1. If an electron drops from $n=5$ to $n=2$, what changes compared with $n=3\to2$?
    A. Longer wavelength
    B. Shorter wavelength
    C. Same wavelength
    D. Cannot determine
    Correct: B

  2. Which statement about emission and absorption is correct?
    A. Different transitions, different wavelengths
    B. Same transitions, same wavelengths, different background intensity
    C. Absorption requires lower-energy photons than emission
    D. Emission lines are always in visible light
    Correct: B

  3. Why is Lyman-alpha not seen by eye in a nebula?
    A. Too weak to detect
    B. Outside visible band (UV)
    C. Hidden by Balmer lines
    D. Forbidden transition
    Correct: B

Short-answer checks

  • Explain, in one paragraph, why line spectra are evidence for quantized atomic energy levels.
  • Use $E_\gamma = hc/\lambda$ to explain why shorter-wavelength lines correspond to higher-energy photons.
  • Describe one way the Bohr atom view is useful and one way it is limited.

Exit ticket

  1. Name one Balmer transition and its approximate wavelength.
  2. State one difference between the Bohr orbit picture and modern orbital interpretation.
  3. In one sentence: how do astronomers identify elements using spectra?

Model notes (deeper)

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Core model

Hydrogen level energies: $$ E_n = -\frac{13.6\ \text{eV}}{n^2} $$

Transition energy: $$ \Delta E = 13.6\ \text{eV}\left(\frac{1}{n_{\rm lower}^2} - \frac{1}{n_{\rm upper}^2}\right) $$

Photon relation: $$ E_\gamma = h\nu = \frac{hc}{\lambda} $$

Implementation notes

  • Shared physics API: packages/physics/src/spectralLineModel.ts
  • Hydrogen transitions are computed (not hardcoded) from Bohr levels.
  • Multi-element lines are empirical catalog entries (NIST-derived teaching subset).
  • Wavelength units: nm (vacuum); energy: eV; frequency: Hz.

Instructional clarifications

  • Core workflow rail framing for class: context $\rightarrow$ mode $\rightarrow$ infer/observe $\rightarrow$ explain pattern.
  • Epistemic split to say explicitly in class: Hydrogen tab is a computed model ($E_n$, $\Delta E$, $\lambda$), while Elements tab is empirical line-catalog behavior used for fingerprint matching.
  • Inverse mode makes this explicit: students enter observed $\lambda$ and infer the best hydrogen transition, which reframes spectroscopy as model-constrained inference.
  • Bohr gives correct hydrogen energy eigenvalues at this level; it does not provide the modern spatial interpretation.
  • Bound-state energies are negative because the zero reference is a free electron + proton at infinite separation.
  • $n=\infty$ is the ionization limit and corresponds to $E=0$.
  • Emission and absorption lines use the same $\Delta E$ values and therefore appear at the same wavelengths.
  • Series convergence comes from shrinking energy-level spacing as $n_{\rm upper}$ increases.
  • Large-$n$ scaling callout: adjacent spacing follows $\Delta E \approx 27.2\ \text{eV}/n^3$, so convergence is structural, not cosmetic.
  • The Bohr-orbit SVG is explicitly not to scale; the energy-ladder view is the quantitative reference.
  • Emission/absorption animations are pedagogical representations of the same transition energies.
  • Hydrogen-tab temperature panel uses relative proxy populations normalized over $n=1,2,3$ plus a qualitative Balmer-strength proxy (Boltzmann excitation times neutral-H proxy), and is labeled as simplified.
  • Verify H-alpha near $656.3\ \text{nm}$.
  • Verify Lyman-alpha near $121.6\ \text{nm}$.
  • Show Balmer convergence trend as $n_{\rm upper}$ increases.
  • Use the series microscope to show line pile-up toward $364.6\ \text{nm}$.
  • Toggle to absorption and confirm wavelength positions are unchanged.
  • Use Mystery reflection gate: students must state one pattern source before reveal.

Backlog

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P0 (blocking before launch-ready promotion)

  • Add a short classroom-run validation log (timing, confusion points, misconceptions observed).
  • Capture screen-reader smoke notes (VoiceOver and NVDA) for transition, mystery-feedback, and copy-lock announcements.

P1 (important, non-blocking for candidate)

  • Expand element preset scaffolds for faster pattern-matching drills (Na D, Ca H/K, Fe line forest).
  • Add an optional projector mode that increases spectrum annotation contrast and label size.

P2 (nice to have)

  • Add a downloadable worksheet variant that auto-fills measured values from snapshot rows.