Physics · Modern Physics

de Broglie Matter Waves

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Bohr ModelWhole-number-fit bridge to Bohr

Key takeaway

de Broglie wavelength is tied to momentum by $\lambda = h / p$, so the main inverse relation is between wavelength and momentum.
On this bounded non-relativistic page, $p = mv$, so increasing either mass or speed increases momentum and shortens the wavelength.

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 per second. It is set by momentum, so larger momentum means smaller wavelength.

Carry the wave-quantum bridge forward

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Whole-number-fit bridge to BohrModern Physics

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.

Reconnect the line evidenceModern Physics

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.

Revisit wavelength as spacingWaves

Wave Speed and Wavelength

Follow one traveling wave across the same medium and connect crest spacing, travel delay, source timing, and the relation v = f lambda on one honest live stage.

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Reference and support

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Open reference and support

Equation snapshotNon-relativistic momentum · de Broglie relationShow 2 equations

Non-relativistic momentum
$p = m v$
On this page, mass and speed combine into one momentum before wavelength is determined.
de Broglie relation
$λ = \frac{h}{p}$
More momentum means a shorter matter wavelength.

Why it behaves this way

Explanation

de Broglie proposed that a particle with momentum has a wavelength, given by $\lambda = h / p$. On this page, that means wavelength is controlled by momentum: if the particle is faster or heavier, its momentum is larger and its wavelength is shorter. That momentum-first view is why electron-scale wavelengths can shape spectra and atomic models while everyday matter waves stay too tiny to notice.

The bench shows this in two linked ways. The strip shows one local wavelength spacing, and the fixed loop shows how many of those wavelengths fit around the same path. When the fit is close to a whole number, the wrapped wave matches up cleanly at the seam. That gives a simple bridge from wave spacing to early quantum ideas without pretending this page is a full quantum-mechanics solver.

Key ideas

01de Broglie wavelength is tied to momentum by $\lambda = h / p$, so the main inverse relation is between wavelength and momentum.

02On this bounded non-relativistic page, $p = mv$, so increasing either mass or speed increases momentum and shortens the wavelength.

03The strip and the loop are two views of the same $\lambda$: when the spacing shrinks on the strip, more wavelengths fit around the loop.

04A whole-number loop fit is a useful bridge toward quantized behavior and the Bohr model, but it is not the full modern quantum picture.

Worked examples

Live matter-wave checks

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the live mass and speed values from the bench. The same settings determine the local spacing strip, the loop-fit count, and both graphs.

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View plans

Example 1 of 2

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 does the page show?

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. Find the momentum

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

2. Convert momentum to wavelength

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

3. Match the numbers to the bench

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.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation has two main stage views: a local strip showing the current matter-wave spacing and a fixed loop showing how many of those wavelengths fit around the same path. Changing mass or speed updates both views together.

Optional overlays mark one wavelength on the strip, show how mass and speed combine into momentum, and compare the loop fit with the nearest whole number. The readout card gives mass, speed, momentum, wavelength, loop length, and fit count.

Graph summary

One graph shows wavelength decreasing as momentum increases. The other shows the loop-fit count increasing as momentum increases because more wavelengths fit around the same fixed path. Hovering a graph previews the corresponding bench state.

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Progress

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Starter track

Step 3 of 5

Modern Physics

de Broglie Matter Waves appears later in this track, so it is cleaner to start from the beginning first.

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