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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.

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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

Why it behaves this way

Explanation

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.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
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.

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Frozen valuesUsing frozen 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 \(\lambda = h / p\)?

Particle mass

1 m_e

Speed

2.2 Mm/s

Momentum

2 10^-24 kg m/s

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?

Make a prediction before you reveal the next step.

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

Check your reasoning against the live bench.

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?

Use the live bench to test the result before moving on.

Accessibility

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.