De Broglie Wavelength
Calculate the de Broglie wavelength of any particle using λ = h/(mv). Select presets for electron, proton, neutron, or enter custom mass and velocity to get the wavelength in m, nm, and pm with interactive charts.
About This Calculator
The De Broglie Wavelength Calculator computes the wavelength associated with any moving particle using the de Broglie relation λ = h/(mv), where h is Planck's constant (6.626×10⁻³⁴ J·s), m is the particle mass in kilograms, and v is the velocity in meters per second. This fundamental equation from quantum mechanics describes the wave-particle duality of matter — the principle that all matter exhibits both particle and wave-like behavior.
Our calculator supports particle presets for the most common subatomic particles: electrons (used in electron microscopes and diffraction experiments), protons (used in particle accelerators), neutrons (used in neutron scattering), and alpha particles (used in Rutherford scattering). You can also enter a custom mass for any particle, making this tool useful for physics students, researchers, and anyone studying quantum mechanics.
The de Broglie wavelength is inversely proportional to both mass and velocity — heavier particles and faster particles have shorter wavelengths. For example, an electron traveling at 10⁶ m/s has a wavelength of approximately 0.73 nanometers, while a proton at the same speed has a wavelength of about 0.4 picometers — nearly 2000 times shorter. This calculator automatically computes the wavelength in meters, nanometers (nm), and picometers (pm) along with the particle's momentum.
About the Formula
The calculation uses the standard de Broglie equation λ = h/p = h/(mv), where momentum p = mv. Planck's constant h = 6.62607015×10⁻³⁴ J·s. Results are displayed with scientific notation for very small values and with detailed breakdowns showing the mass, velocity, momentum, and wavelength in multiple units.
Frequently Asked Questions
What is the de Broglie wavelength equation?
The de Broglie wavelength equation is λ = h/(mv), where λ is the wavelength in meters, h is Planck's constant (6.626×10⁻³⁴ J·s), m is the particle mass in kg, and v is the particle velocity in m/s. It describes the wave-like nature of matter.
What is the de Broglie wavelength of an electron moving at 1% of the speed of light?
An electron (mass 9.109×10⁻³¹ kg) moving at 1% of light speed (2.998×10⁶ m/s) has a de Broglie wavelength of approximately 0.242 nm or 242 pm. This is calculated using λ = h/(mv) = 6.626×10⁻³⁴ / (9.109×10⁻³¹ × 2.998×10⁶).
How does mass affect the de Broglie wavelength?
The de Broglie wavelength is inversely proportional to mass. Heavier particles have shorter wavelengths at the same velocity. For example, a proton has about 1836 times the mass of an electron, so its de Broglie wavelength is about 1836 times shorter at the same speed.
Can macroscopic objects have a de Broglie wavelength?
Yes, all matter has a de Broglie wavelength, but for macroscopic objects the wavelength is extremely small and undetectable. A 1 kg object moving at 1 m/s has a de Broglie wavelength of about 6.626×10⁻³⁴ m — far too small to measure. Wave-like behavior is only observable at the atomic and subatomic scale.
What is the de Broglie wavelength used for?
The de Broglie wavelength is fundamental in quantum mechanics. It explains electron diffraction in crystals (used in transmission electron microscopy), determines the resolution of electron microscopes, and is essential for understanding quantum phenomena like electron interference and quantum tunneling.
How does velocity affect de Broglie wavelength?
The de Broglie wavelength is inversely proportional to velocity. As a particle's velocity increases, its wavelength decreases. An electron at 10⁶ m/s has a wavelength of about 0.73 nm, while at 10⁷ m/s it shrinks to about 0.073 nm.
What units are used for de Broglie wavelength?
The de Broglie wavelength is measured in meters (SI unit), but due to the extremely small wavelengths of particles, it is more commonly expressed in nanometers (nm, 10⁻⁹ m) or picometers (pm, 10⁻¹² m). Electron wavelengths are typically in the range of 0.01 to 10 nm.
Who proposed the de Broglie wavelength?
French physicist Louis de Broglie proposed the wave-particle duality of matter in his 1924 PhD thesis, suggesting that all particles have a wavelength given by λ = h/p. For this breakthrough, he won the Nobel Prize in Physics in 1929, laying the foundation for wave mechanics and quantum theory.