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Concept module

Bohr Model

Use a compact hydrogen bench to connect quantized energy levels, allowed transitions, and named spectral-line series while staying clear that Bohr is a useful historical model rather than the final quantum description.

Interactive lab

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

Time

0.00 s / 5.40 sLiveThe hydrogen-series graph stays wavelength-based while the time rail inspects one active Bohr transition and its matching reverse-wavelength cue.

0.00 s5.40 s

Bohr Model

A bounded Bohr bench keeps hydrogen radius scaling, quantized energies, and spectral-line wavelengths on one shared surface.

Live setup

Graphs

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

Hydrogen series spectrum

Shows the current hydrogen series as a set of narrow line peaks from ultraviolet through infrared with the active transition highlighted on the same wavelength axis.

wavelength (nm): 90 to 1.90e3relative line strength: 0 to 1.15

Balmer line map

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

Controls

Adjust the physical parameters and watch the motion respond.

Upper level

n_{i}

Choose the starting Bohr level n_i.

Lower level

n_{f}

Choose the lower level n_f, which selects Lyman, Balmer, or Paschen.

Show reverse excitation

m

Flip the active jump to the matching absorbed-photon case.

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 reverse excitation flips the arrow but keeps the same wavelength because the allowed energy difference did not change.

Try this

Flip from Balmer alpha to Balmer reverse excitation.

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.

n_{i}

Upper level

Chooses which allowed upper hydrogen level starts the current transition.

Graph: Hydrogen series spectrumOverlay: Line labelsOverlay: Radius ruleOverlay: Series family

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 radius map, energy ladder, line strip, and spectrum graph stay on the same compact bench.

MisconceptionPrompt 1 of 3

Graph: Hydrogen series spectrum

Switching to reverse excitation flips the arrow but keeps the same wavelength because the allowed energy difference did not change.

Try this

Flip from Balmer alpha to Balmer reverse excitation.

Why it matters

It keeps emission and absorption locked to one honest gap story.

Control: Show reverse excitationGraph: Hydrogen series spectrumOverlay: Reverse wavelength 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

Radius rule

Shows how the allowed Bohr radii expand like n^2.

What to notice

The higher selected orbit stretches much farther from the nucleus than the lower one.

Why it matters

It keeps the historical orbit picture tied to the same quantized ladder instead of floating as a separate diagram.

Control: Upper levelGraph: Hydrogen series spectrumEquation

n_{i}

Challenge mode

Use the same hydrogen bench for compact transition and series targets instead of widening into a full atomic-physics engine.

0/2 solved

TargetCore

2 of 8 checks

Match the reverse UV excitation

Starting from Lyman alpha emission, switch to the matching reverse excitation from the ground level while keeping the same ultraviolet wavelength.

Graph-linkedGuided start2 hints

Suggested start

Use the reverse-transition cue so arrow direction does not trick you into picking a different wavelength.

Matched

Open the Hydrogen series spectrum graph.

Hydrogen series spectrum

Matched

Keep the Reverse wavelength lock visible.

Pending

Keep lower level between 1 and 1.

Pending

Keep upper level between 2 and 2.

Pending

Keep excitation flag between 1 and 1.

Pending

Keep wavelength nm between 121 nm and 123 nm.

656.39 nm

Pending

Keep photon energy ev between 10.1 eV and 10.3 eV.

1.89 eV

Pending

Keep active visible flag between 0 and 0.

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

At display t = 0 s, the Bohr model is showing emission for 3 -> 2. The hydrogen energy gap is 1.89 eV, so the matching wavelength is 656.39 nm in the visible. The selected Balmer family crowds toward 364.66 nm because the higher allowed energies bunch up near zero. This remains a bounded historical hydrogen model rather than the final quantum description.

Equation detailsDeeper interpretation, notes, and worked variable context.

Bohr energy levels

Hydrogen's allowed Bohr energies get closer together as n increases.

E_{n} = - \frac{13.6 eV}{n ^{2}}

n_{f}

Lower level 2

Allowed transition energy

A hydrogen photon comes from the difference between two allowed levels with n_i > n_f.

Δ E = 13.6 eV (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})

n_{i}

Upper level 3

n_{f}

Lower level 2

m

Reverse excitation Off

Gap to wavelength

Shorter wavelengths correspond to larger allowed Bohr gaps.

λ = \frac{h c}{Δ E}

n_{i}

Upper level 3

n_{f}

Lower level 2

m

Reverse excitation Off

Bohr radius scaling

Higher allowed Bohr orbits sit farther from the nucleus very quickly.

r_{n} \propto n^{2}

n_{i}

Upper level 3

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 4 of 50 / 5 complete

Modern Physics

Earlier steps still set up Bohr Model.

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

Previous step: de Broglie Matter Waves.

Start from track beginning

Short explanation

What the system is doing

The Bohr model is a bounded historical hydrogen model: it gives electrons only certain allowed energy levels, so light comes from discrete transitions rather than from any arbitrary orbital drop. That makes it a strong bridge from observed line spectra to quantized atomic structure without pretending to be the final quantum description.

This module keeps one compact bench with a radius map, an energy ladder, a hydrogen line map, and one wavelength graph. The selected transition, its wavelength, its series family, its reverse excitation case, the worked examples, quick tests, and challenge checks all stay tied to that same live state.

Key ideas

01For hydrogen in the Bohr model, the allowed energies follow E_n = -13.6 eV / n^2, so only certain transition gaps exist.

02Holding the lower level fixed creates named hydrogen series such as Lyman, Balmer, and Paschen.

03Within one series, higher starting levels crowd the lines toward a series limit because the upper energies bunch closer together.

04This page treats Bohr as a useful historical and conceptual model for hydrogen spectral lines, not as the final quantum-mechanical picture.

Live Bohr checks

Solve the exact state on screen.

Use the current hydrogen transition directly from the live bench. The same levels, graph, overlays, and readout card drive each worked result.

Live valuesFollowing current parameters

For the current transition 3 -> 2, what photon energy and wavelength belong to this Bohr jump?

n_{i}

Upper level

n_{f}

Lower level

Δ E

Transition energy

1.89 eV eV

λ

Photon wavelength

656.39 nm nm

1. Identify the live jump

The bench is currently showing 3 -> 2, so the electron changes between n = 3 and n = 2.

2. Read the quantized gap

That allowed hydrogen gap is 1.89 eV on the live ladder and readout card.

3. Convert the gap to a photon wavelength

Using

λ = h c /Δ E

, this jump gives 656.39 nm in the Visible.

Current transition

Δ E = 1.89 e V, λ = 656.39 nm, V i s ib l e

This Balmer transition lands in visible red, so the line sits inside the same wavelength window the graph and strip highlight together.

Hydrogen-line checkpoint

Why do 3 -> 2 emission and 2 -> 3 excitation use the same wavelength on this page even though one arrow points down and the other points up?

Prediction prompt

Answer from the allowed energy gap, not from arrow direction alone.

Check your reasoning

They use the same wavelength because both processes involve the same energy difference between the same two allowed levels. Emission releases that photon energy, and excitation requires that same photon energy.

The direction changes whether the atom gives the photon energy away or absorbs it, but the magnitude of the allowed gap stays fixed.

Common misconception

If the electron can orbit the nucleus, it should be able to fall from any radius to any other and emit any color you want.

In the bounded Bohr model, only specific energy levels are allowed, so only specific transition gaps and wavelengths appear.

Modern quantum mechanics replaces the literal orbit picture, but the quantized-level idea still explains why hydrogen line spectra are discrete.

Quick test

Reasoning

Question 1 of 4

Answer from the live hydrogen-level story, not from disconnected historical slogans.

Why does the Bohr-model page show discrete hydrogen lines instead of every wavelength?

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 compact Bohr-model hydrogen bench with a radius map on the left, an energy ladder in the middle, and a hydrogen line strip on the right. A highlighted arrow marks the active transition, and a matching wavelength marker appears on the strip and graph.

Optional overlays label the line family, the allowed wavelengths, the n squared radius scaling, and the matching reverse-excitation wavelength. The readout card summarizes the current mode, series name, active level pair, photon energy, wavelength, series limit, and radius ratio.

Graph summary

The graph plots relative line strength against wavelength across ultraviolet, visible, and infrared regions for the selected hydrogen series. Narrow peaks mark the allowed series lines, and the active transition is read from the same wavelength axis used by the strip.

Carry the hydrogen 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-fit bridge behind BohrModern Physics

Bohr Model

See each variable before you move it.

Radius rule

Match the reverse UV excitation

Modern Physics

What the system is doing

Solve the exact state on screen.

For the current transition 3 -> 2, what photon energy and wavelength belong to this Bohr jump?

Why does the Bohr-model page show discrete hydrogen lines instead of every wavelength?

Keep moving through the concept map.

de Broglie Matter Waves

Atomic Spectra

Radioactivity and Half-Life