NSW · HSCModule 8
De Broglie wavelength calculator
λ = h/p. Pick a particle (electron, proton, neutron, alpha) or enter your own mass, then give the velocity.
Inputs
Result
de Broglie wavelength λ
7.274e-10m
Momentum p = mv
9.109e-25kg·m/s
λ = h/p, with h = 6.626 × 10⁻³⁴ J·s. Massive everyday objects have wavelengths far below any atomic scale, which is why we don't see wave behaviour in classical mechanics.
How this calculator works
The calculator multiplies mass by velocity to get momentum, then divides Planck's constant by momentum to get the de Broglie wavelength. The formula uses classical p = mv; for v close to c, use the relativistic momentum p = γmv.
Common questions
- What is the de Broglie wavelength?
- Every particle with momentum p has an associated matter wavelength λ = h/p, where h is Planck's constant. For an electron at 1% of c, λ is about 0.24 nm (comparable to atomic spacing).
- Why don't we see wave behaviour in everyday objects?
- Because their de Broglie wavelengths are vanishingly small. A cricket ball at 30 m/s has λ ≈ 10⁻³⁴ m, far below any measurable scale.
- How does this relate to Bohr's atom?
- Bohr's circular electron orbits correspond to standing matter waves: an integer number of de Broglie wavelengths fits around the circumference. This gives quantised angular momentum L = nh/(2π).
- What is electron diffraction?
- When electrons of de Broglie wavelength near the atomic spacing pass through a crystal, they diffract like X-rays. The Davisson-Germer experiment in 1927 confirmed the de Broglie hypothesis.