de Broglie Wavelength Calculator
Calculate matter-wave wavelength from particle mass and velocity using λ = h/(mv). Includes electron, proton, and neutron presets.
What Is the de Broglie Wavelength?
Louis de Broglie proposed that all matter has wave-like properties. The de Broglie wavelength \(\lambda\) relates a particle's momentum to a characteristic wavelength, bridging classical and quantum mechanics.
de Broglie Formula
$$\lambda = \frac{h}{p} = \frac{h}{mv}$$\(h = 6.626 \times 10^{-34}\) J·s is Planck's constant, \(m\) is mass in kg, and \(v\) is velocity in m/s. An electron at \(10^6\) m/s has a wavelength on the order of nanometers.
Real-World Applications
de Broglie wavelengths explain electron diffraction, electron microscopy, quantum tunneling, and the behavior of matter waves in interferometry experiments.
Frequently Asked Questions
Why do heavier particles have shorter wavelengths?
Wavelength is inversely proportional to momentum. At the same speed, a heavier particle has more momentum and therefore a shorter wavelength.
Can everyday objects have a de Broglie wavelength?
Yes, but macroscopic objects have wavelengths so tiny they are unobservable. Quantum effects dominate at atomic and subatomic scales.
What particle presets are available?
Electron, proton, and neutron rest masses are built in. Choose custom to enter any mass in kilograms.
Is relativistic mass included?
This calculator uses classical momentum \(p = mv\). For speeds approaching the speed of light, relativistic corrections are needed.
How does this differ from Compton wavelength?
Compton wavelength uses \(h/(mc)\) for a particle at rest. de Broglie wavelength depends on actual velocity through \(h/(mv)\).
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