Starter track
Step 3 of 50 / 5 completeModern 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.
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
Loading the live simulation bench.
Progress
Not startedMastery: NewLocal-firstStart 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
Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.
Saved setups
Premium keeps named exact-state study setups in your account while stable concept links stay public below.
Checking saved setup access.
This concept can keep using stable links while the saved-setups capability resolves for this browser.
Copy current setup
Stable concept and section links stay public below while exact-state setup sharing stays behind premium.
Stable links
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.
Worked example
Read the full frozen walkthrough.
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.
Live worked examples are available on Premium. You can still read the full frozen walkthrough on the free tier.
View plansFrozen 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?
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
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 spacingOscillations
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.