λ de Broglie

The de Broglie wavelength calculator determines the wavelength associated with moving particles based on quantum theory. Louis de Broglie's hypothesis states that all matter exhibits wave-like properties, with wavelength λ = h/p, where h is Planck's constant and p is momentum. This principle is foundational in quantum mechanics and wave-particle duality studies.

The tool calculates λ by either directly using momentum (p = mass × velocity) or by applying the formula λ = h/(m·v). Input units must be consistent: mass in kg, velocity in m/s, and Planck's constant as 6.626×10⁻³⁴ J·s. Results are typically on the order of picometers or smaller, highlighting the quantum scale of this phenomenon.

This calculator is commonly used in electron diffraction experiments, particle physics, and nanoscale material studies. In macroscopic objects, the de Broglie wavelength is negligible due to large masses, but it becomes significant for subatomic particles like electrons in electron microscopes or accelerators.

Key considerations: Ensure momentum is calculated correctly (mass×velocity), and remember that relativistic effects become relevant at velocities near the speed of light. For educational purposes or low-speed applications, the classical formula suffices.