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Concept module

de Broglie Matter Waves

Use one compact matter-wave bench to see how particle momentum sets wavelength, why heavier or faster particles get shorter wavelengths, and how whole-number loop fits form a bounded bridge toward early quantum behavior.

Interactive lab

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

A compact bench keeps local matter-wave spacing next to one fixed loop so momentum, wavelength, and whole-number fits stay on the same bounded visual story.

Live setup

Graphs

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

Wavelength vs momentum

Shows the inverse de Broglie relation directly: larger momentum means shorter wavelength.

momentum (10^-24 kg m/s): 0.73 to 10.49wavelength (nm): 0 to 1

Matter wavelength

Hover or scrub to link the graph back to the stage.momentum (10^-24 kg m/s) / wavelength (nm)

Controls

Adjust the physical parameters and watch the motion respond.

Particle mass

m

1 m_e

Scales the particle mass in electron-mass units.

Speed

v

2.2 Mm/s

Changes the particle speed while the bench keeps the same bounded de Broglie relation.

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.

Graph readingPrompt 1 of 2

Notice that hovering either response graph previews the same bench at that momentum instead of inventing a disconnected quantum example.

Try this

Hover farther to the right on either graph and compare the tighter local spacing with the higher loop count.

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.

m

Particle mass

1 m_e

A heavier particle at the same speed has larger momentum, so its matter wavelength gets shorter.

Graph: Wavelength vs momentumGraph: Loop fit vs momentumOverlay: Momentum linkOverlay: Whole-number fit

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 cue at a time so the local spacing sketch, the loop seam, and the response graphs stay tied to the same momentum story.

Graph readingPrompt 1 of 2

Graph: Wavelength vs momentum

Notice that hovering either response graph previews the same bench at that momentum instead of inventing a disconnected quantum example.

Try this

Hover farther to the right on either graph and compare the tighter local spacing with the higher loop count.

Why it matters

The graphs and the bench are two views of one momentum-based state.

Graph: Wavelength vs momentumGraph: Loop fit vs momentumOverlay: Momentum linkOverlay: Whole-number fit

Guided overlays

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

3 visible

Overlay focus

Wavelength guide

Marks one local crest-to-crest spacing on the matter-wave strip.

What to notice

As momentum grows, the marked wavelength shortens on the strip while the loop count rises on the right.

Why it matters

It keeps wavelength visible as a spatial spacing instead of reducing the idea to algebra alone.

Control: SpeedGraph: Wavelength vs momentumEquation

v

Challenge mode

Use the same bounded bench for compact whole-number-fit targets.

0/2 solved

TargetCore

5 of 6 checks

Find the one-fit electron

Starting from Slow electron, tune the speed until the fixed loop is close to one wavelength long without changing the particle mass.

Graph-linkedGuided start2 hints

Suggested start

Use the loop-fit graph and the seam cue together.

Pending

Open the Loop fit vs momentum graph.

Wavelength vs momentum

Matched

Keep the Whole-number fit visible.

Matched

Keep mass multiple between 1 m_e and 1 m_e.

1 m_e

Matched

Keep speed mms between 2.1 Mm/s and 2.3 Mm/s.

2.2 Mm/s

Matched

Keep wavelength nm between 0.315 nm and 0.35 nm.

0.33 nm

Matched

Keep fit count between 0.95 and 1.05.

1.01

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

A 1 m_e particle moving at 2.2 Mm/s has momentum 2 x10^-24 kg m/s, so its de Broglie wavelength is 0.33 nm. That is close to a whole-number fit of n = 1, so the loop seam nearly closes after 1 wavelengths. This page keeps that bridge bounded and non-relativistic: momentum changes the wavelength, and whole-number loop fits are used only as an intuition-first hint toward quantum behavior.

Equation detailsDeeper interpretation, notes, and worked variable context.

Non-relativistic momentum

In this bounded page, mass and speed combine into one momentum that sets the matter wavelength.

p = m v

m

Particle mass 1 m_e

v

Speed 2.2 Mm/s

de Broglie relation

Matter wavelength decreases when momentum increases.

λ = \frac{h}{p}

v

Speed 2.2 Mm/s

Mass-speed form

For the same particle type, higher speed means shorter wavelength. For the same speed, a heavier particle also has a shorter wavelength.

λ = \frac{h}{m v}

m

Particle mass 1 m_e

v

Speed 2.2 Mm/s

Whole-number loop fit

A clean loop seam appears when a whole number of wavelengths fits around the fixed path.

N = \frac{L}{λ}

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 3 of 50 / 5 complete

Modern Physics

Earlier steps still set up de Broglie Matter Waves.

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

Previous step: Atomic Spectra.

Start from track beginning

Short explanation

What the system is doing

de Broglie's proposal gives particles a wavelength through their momentum. In this bounded page, the wave idea is used only for that bridge: a faster or heavier particle has larger momentum, so its wavelength gets shorter instead of longer.

The bench stays compact and visually honest. One panel shows the local matter-wave spacing, and one fixed loop asks how many wavelengths fit around the same path. That is enough to connect wave spacing to early quantum behavior without pretending this page is a full quantum-mechanics solver.

Key ideas

01Matter waves are tied to momentum through \(\lambda = h / p\), so the key inverse relation is between wavelength and momentum, not between wavelength and distance traveled each second.

02For the bounded non-relativistic model here, \(p = mv\), so raising either mass or speed makes the wavelength shorter.

03A fixed loop that fits a whole number of wavelengths gives a clean seam match. That whole-number-fit cue is a useful bridge toward quantized behavior and the Bohr branch, even though it is not the full modern quantum picture.

Live matter-wave checks

Solve the exact state on screen.

Use the current particle mass and speed directly from the live bench. The same settings drive the local spacing sketch, the loop-fit cue, and the response graphs.

Live valuesFollowing current parameters

For the current particle mass \(1\,m_e\) and speed \(2.2\,\mathrm{Mm/s}\), what momentum and de Broglie wavelength follow from \(p = mv\) and \(\lambda = h / p\)?

m

Particle mass

1 m_e

v

Speed

2.2 Mm/s

p

Momentum

2 10^-24 kg m/s

λ

Matter wavelength

0.33 nm

1. Combine mass and speed into one momentum

In this bounded model, the live settings give \(p = mv = 2\times10^{-24}\,\mathrm{kg\,m/s}\).

2. Use the de Broglie relation

Then \(\lambda = h / p\), so the current matter wavelength is \(0.33\,\mathrm{nm}\).

3. Read the bench honestly

That wavelength is the spacing you see on the local strip, and the same \(\lambda\) is what the loop panel tests for a whole-number fit.

Current matter wavelength

\(p = 2\times10^{-24}\,\mathrm{kg\,m/s}, \quad \lambda = 0.33\,\mathrm{nm}\)

The momentum is still modest here, so the wavelength stays comparatively long and the local spacing remains easy to see on the strip.

Whole-number-fit checkpoint

Two electrons use the same fixed loop. Electron B moves about twice as fast as Electron A, while the mass stays the same. Which electron is closer to fitting more whole wavelengths around the loop, and why?

Prediction prompt

Answer from momentum and wavelength first, not from how long the path looks.

Check your reasoning

Electron B is closer to fitting more whole wavelengths because the larger speed gives larger momentum, and larger momentum means a shorter de Broglie wavelength.

The loop length stays fixed, so shrinking \(\lambda\) increases \(N = L / \lambda\). The faster electron therefore fits more wavelengths around the same path.

Common misconception

A faster particle should have a longer wavelength because it covers more distance each second.

de Broglie wavelength is not set by distance traveled in one second. It is set by momentum, so larger momentum means smaller wavelength.

This page also does not treat the particle like a little water wave. It uses wavelength as a bounded bridge between wave ideas and quantum behavior.

Quick test

Variable effect

Question 1 of 4

Answer from the live momentum-wavelength link, not from loose wave analogies.

For the same particle mass, you increase the speed. What should happen next?

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 de Broglie matter-wave bench with a local spacing strip on the left and one fixed loop on the right. The strip shows the current matter wavelength along a short path segment, while the loop shows how many wavelengths fit around a fixed Bohr-like circumference.

Optional overlays mark one wavelength on the strip, the momentum link from mass and speed, and the whole-number loop fit. The readout card summarizes mass, speed, momentum, wavelength, the fixed loop length, and the current fit count.

Graph summary

The wavelength-versus-momentum graph shows the inverse de Broglie relation directly. The loop-fit graph shows how a fixed loop holds more wavelengths as momentum rises. Hovering either graph previews the same bench at that momentum.

Carry the wave-quantum bridge 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.

Whole-number-fit bridge to BohrModern Physics

de Broglie Matter Waves

See each variable before you move it.

Wavelength guide

Find the one-fit electron

Modern Physics

What the system is doing

Solve the exact state on screen.

For the current particle mass \(1\,m_e\) and speed \(2.2\,\mathrm{Mm/s}\), what momentum and de Broglie wavelength follow from \(p = mv\) and \(\lambda = h / p\)?

For the same particle mass, you increase the speed. What should happen next?

Keep moving through the concept map.

Bohr Model

Atomic Spectra

Wave Speed and Wavelength