de Broglie Wavelength Calculator
Find the quantum (matter-wave) wavelength of a moving particle from its mass and speed using λ = h ÷ (m·v).
How it works
λ = h ÷ p = h ÷ (m·v) · with h = 6.626×10⁻³⁴ J·s
De Broglie proposed that every moving particle has a wavelength λ = h/p, inversely proportional to its momentum. For everyday objects the momentum is so large that the wavelength is unimaginably tiny and no wave behaviour shows — but for electrons and other light, slow particles it becomes comparable to atomic spacings, which is why electrons diffract and why electron microscopes work. The heavier or faster the particle, the shorter its wavelength.
Worked example
An electron (m = 9.11×10⁻³¹ kg) moving at 1×10⁶ m/s has momentum p = 9.11×10⁻³¹ × 10⁶ = 9.11×10⁻²⁵ kg·m/s. Its wavelength is λ = 6.626×10⁻³⁴ / 9.11×10⁻²⁵ ≈ 7.27×10⁻¹⁰ m, about 0.73 nm — comparable to the spacing of atoms in a crystal.
Sources: Matter wave — Wikipedia
Frequently asked questions
Why don’t everyday objects show a wavelength?
Their momentum is enormous, so λ = h/p is fantastically small — around 10⁻³⁴ m for a thrown ball, far below anything measurable. Wave behaviour only becomes noticeable for tiny particles with small momenta.
How does the de Broglie wavelength enable electron microscopes?
Fast electrons have wavelengths thousands of times shorter than visible light, and resolution improves with shorter wavelength. That lets electron microscopes resolve features far smaller than any light microscope can.
Is this formula valid at very high speeds?
The simple λ = h/(m·v) uses non-relativistic momentum, good when the speed is well below light speed. Near the speed of light you must use the relativistic momentum p = γm·v instead.
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This calculator is for educational purposes. Double-check important results before acting on them.