Key relationship
λ=h/p; p=√[K(K+2mc²)]/c; K=eV. Low-energy limit λ=h/√(2meV).
Physics · Class 12
de Broglie wavelength
Dual Nature of Radiation & Matter
Matter wavelength is set by momentum. Equal accelerating voltage gives equal kinetic energy to electron and proton, but their different masses produce different momenta and wavelengths.
Open the interactive experiment →de Broglie wavelength
பொருள் அலையின் அலைநீளம் h/p. ஒரே மின்னழுத்தத்தில் வேறுபட்ட நிறைகள் வேறுபட்ட உந்தங்களையும் அலைநீளங்களையும் தரும்.
Key notes, relationships and model limits
Remember
Matter wavelength is set by momentum. Equal accelerating voltage gives equal kinetic energy to electron and proton, but their different masses produce different momenta and wavelengths.
Common trap
Matter wavelength is not the physical diameter of the particle.
Model limits
Initially stationary singly charged particle; collision-free acceleration. Relativistic energy-momentum relation used so the high-voltage correction remains consistent.
What you will learn
Connect particle momentum to a measurable matter-wave scale.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
A150 V electron has wavelength about0.100 nm.
Why this matters
The model connects de broglie wavelength with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
In the nonrelativistic limit, fourfold voltage changes λ to?
- Four times
- Half
- Twice
Read the explanation
Momentum scales as √V, so wavelength scales as1/√V.
Course connection: Class XII Chapter 11. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.