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Concept module

Atomic Spectra

Link discrete emission and absorption lines to allowed energy-level gaps with one compact ladder-and-spectrum bench that keeps transitions, wavelengths, and mode changes tied together.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 5.40 sLiveThe spectrum graph stays wavelength-based while the time rail inspects one active transition at a time on the same energy ladder.

0.00 s5.40 s

Atomic Spectra

A compact energy ladder and spectrum bench keep discrete level gaps, observed lines, and emission-versus-absorption mode on one honest surface.

Live setup

Graphs

Switch graph views without breaking the live stage and time link.

Observed spectrum

Shows the current discrete line pattern across ultraviolet, visible, and infrared wavelengths with a continuum reference for the absorption case.

wavelength (nm): 110 to 1.20e3relative intensity: 0 to 1.15

Emission spectrumContinuum reference

Hover or scrub to link the graph back to the stage.wavelength (nm) / relative intensity

Controls

Adjust the physical parameters and watch the motion respond.

2 to 1 gap

Δ E_{2 \to 1}

1.9 eV

Sets the lowest allowed gap.

3 to 2 gap

Δ E_{3 \to 2}

2.6 eV

Sets the middle allowed gap.

4 to 3 gap

Δ E_{4 \to 3}

2.7 eV

Sets the highest allowed gap.

Show absorption case

m

Switch between bright emission lines and dark absorption notches without changing the allowed wavelengths.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

MisconceptionPrompt 1 of 3

Switching to absorption does not move the allowed wavelengths. It changes the same lines from bright peaks into dark notches.

Try this

Flip between the hydrogen-like emission and absorption presets.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

Δ E_{2 \to 1}

2 to 1 gap

1.9 eV

Moves the lowest visible or infrared line and any larger jump that includes level 1.

Graph: Observed spectrumOverlay: Transition pairsOverlay: Quantized spacing

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one prompt at a time so the ladder, the spectrum strip, and the wavelength graph stay on the same compact bench.

MisconceptionPrompt 1 of 3

Graph: Observed spectrum

Switching to absorption does not move the allowed wavelengths. It changes the same lines from bright peaks into dark notches.

Try this

Flip between the hydrogen-like emission and absorption presets.

Why it matters

It keeps emission and absorption tied to the same atomic structure.

Control: Show absorption caseGraph: Observed spectrumOverlay: Mode lockOverlay: Line labels

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

Transition pairs

Links the active ladder jump directly to its wavelength in the spectrum strip.

What to notice

The active arrow and the active line move together because they are two views of the same energy change.

Why it matters

It prevents the ladder and the spectrum from becoming disconnected pictures.

Control: 2 to 1 gapControl: 3 to 2 gapControl: 4 to 3 gapGraph: Observed spectrumEquation

Δ E_{2 \to 1}

Equation

Δ E_{3 \to 2}

Equation

Δ E_{4 \to 3}

Challenge mode

Use the same ladder-and-spectrum bench for line-pattern targets instead of switching to a separate spectroscopy tool.

0/2 solved

TargetCore

5 of 7 checks

Keep only two visible emission lines

Starting from Hydrogen-like emission, tune the gaps so only two visible lines remain while the spectrum still stretches from blue-visible to red-visible wavelengths.

Graph-linkedGuided start2 hints

Suggested start

Use the graph and the strip together so you can count visible lines and watch where they land.

Matched

Open the Observed spectrum graph.

Observed spectrum

Matched

Keep the Transition pairs visible.

Matched

Keep mode flag between 0 and 0.

Pending

Keep visible line count between 2 and 2.

Matched

Keep shortest visible wavelength nm between 430 nm and 520 nm.

459.2 nm

Matched

Keep longest visible wavelength nm between 620 nm and 720 nm.

652.55 nm

Pending

Keep min visible separation nm between 120 nm and 260 nm.

17.66 nm

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At display t = 0 s, the active level pair 4 -> 1 spans 7.2 eV, so it corresponds to the wavelength 172.2 nm as a bright emission line against a dark background. The current gap pattern produces 3 visible lines, and the spectrum stays discrete because only the allowed level differences 1.9 eV, 2.6 eV, and 2.7 eV are available.

Equation detailsDeeper interpretation, notes, and worked variable context.

Energy carried by one spectral line

Each line corresponds to one photon energy that matches one allowed level difference.

Δ E = h f = \frac{h c}{λ}

Δ E_{2 \to 1}

2 to 1 gap 1.9 eV

Δ E_{3 \to 2}

3 to 2 gap 2.6 eV

Δ E_{4 \to 3}

4 to 3 gap 2.7 eV

Wavelength from an energy gap

Bigger level gaps give shorter wavelengths; smaller gaps give longer wavelengths.

λ = \frac{h c}{Δ E}

Δ E_{2 \to 1}

2 to 1 gap 1.9 eV

Δ E_{3 \to 2}

3 to 2 gap 2.6 eV

Δ E_{4 \to 3}

4 to 3 gap 2.7 eV

Combined jump

A larger jump across several levels adds the intermediate gaps together.

Δ E_{4 \to 1} = Δ E_{4 \to 3} + Δ E_{3 \to 2} + Δ E_{2 \to 1}

Δ E_{2 \to 1}

2 to 1 gap 1.9 eV

Δ E_{3 \to 2}

3 to 2 gap 2.6 eV

Δ E_{4 \to 3}

4 to 3 gap 2.7 eV

Shared allowed wavelengths

Emission and absorption line positions match because both use the same allowed level differences.

λ_{abs} = λ_{emit}

m

Absorption mode Off

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 2 of 50 / 5 complete

Modern Physics

Earlier steps still set up Atomic Spectra.

1. Photoelectric Effect2. Atomic Spectra3. de Broglie Matter Waves4. Bohr Model+1 more steps

Previous step: Photoelectric Effect.

Start from track beginning

Short explanation

What the system is doing

Atomic spectra are the bounded modern-physics case where light does not come out in every color. When an atom changes between allowed energy levels, it can emit or absorb only photons whose energy matches one of those level gaps, so the spectrum breaks into discrete lines instead of a smooth rainbow.

This module keeps one energy ladder, one observed spectrum strip, one wavelength graph, and one shared set of readouts. The same gaps drive the stage, overlays, worked examples, challenge checks, compare mode, quick test, and read-next cues, so the learner keeps one honest link between energy changes and spectral lines instead of drifting into a detached derivation page.

Key ideas

01Each spectral line comes from one allowed energy difference, not from any arbitrary wavelength.

02Larger energy gaps make shorter-wavelength photons, while smaller gaps make longer-wavelength photons.

03Emission and absorption use the same allowed wavelengths because they come from the same level differences.

04This compact ladder is a bounded precursor to later Bohr-style level models: it emphasizes line positions and energy differences without claiming full atomic structure.

Live spectra checks

Solve the exact state on screen.

Use the current ladder and spectrum state directly from the live bench. The same gaps and mode setting drive the stage, the spectrum graph, the overlays, and the worked result.

Live valuesFollowing current parameters

With gaps 1.9 eV, 2.6 eV, and 2.7 eV, which visible lines should the current ladder produce?

Δ E_{2 \to 1}

Level 2 to 1 gap

1.9 eV eV

Δ E_{3 \to 2}

Level 3 to 2 gap

2.6 eV eV

Δ E_{4 \to 3}

Level 4 to 3 gap

2.7 eV eV

1. Convert the 2 -> 1 gap to a wavelength

For the current ladder,

Δ E_{2 \to 1} = 1.9 e V

, so the 2 -> 1 line sits near 652.55 nm.

2. Convert another allowed gap

The 3 -> 2 gap is 2.6 eV, so that line lands near 476.86 nm.

3. Read the visible pattern honestly

On the live spectrum, the current gap set gives 3 visible lines between 459.2 nm and 652.55 nm.

Current visible pattern

λ_{2 \to 1} = 652.55 nm, λ_{3 \to 2} = 476.86 nm, 3 v i s ib l e l in es

The current lower-level gaps create at least two visible lines, and the smaller gap 1.9 eV lands at the longer visible wavelength 652.55 nm.

Line-pattern checkpoint

A spectrum shows only a few narrow lines instead of every visible color. What is the strongest bounded explanation on this page?

Prediction prompt

Answer from the allowed energy gaps, not from the color labels alone.

Check your reasoning

The atom can change only between allowed energy levels, so it can emit or absorb only the photon energies that match those level differences.

Discrete level gaps create discrete photon energies. The page stays bounded by showing only that line-pattern logic, without claiming a full atom-by-atom derivation.

Common misconception

Emission lines and absorption lines should appear at different wavelengths because one process sends light out and the other takes light in.

The same allowed level gaps set both processes, so the allowed wavelengths match.

What changes is the appearance of the spectrum: emission gives bright lines, while absorption removes those same wavelengths from a background continuum.

Quick test

Reasoning

Question 1 of 4

Answer from the live line-spectrum logic, not from disconnected labels.

Why does this bounded atomic-spectrum page show discrete lines instead of a smooth visible rainbow?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a four-level energy ladder on the left and a compact observed-spectrum strip on the right. Colored arrows mark allowed level changes, and the active transition is linked to a matching wavelength in the spectrum strip.

Optional overlays can label each line, lock emission and absorption to the same wavelengths, and call out why only a few wavelengths appear. The readout card summarizes the current mode, active level pair, photon energy, wavelength, visible-line count, visible-band edges, and minimum visible spacing.

Graph summary

The spectrum graph plots relative intensity against wavelength from ultraviolet through visible to infrared. In emission mode, the graph shows narrow bright peaks on a dark baseline. In absorption mode, it shows dark notches carved out of a flat continuum reference at those same wavelengths.

Carry the line story forward

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Wave bridge to quantizationModern Physics