The De Broglie Equation calculator computes the wavelength of a particle based on the Planck's Constant and momentum (p = m•v).
INSTRUCTIONS: Choose units and enter the following:
- (m) Mass of Particle
- (v) Velocity of Particle
Wavelength (λ): The calculator returns the DeBrogile wavelength in nanometers (nm). However, this can be automatically converted to other length units (e.g. angstroms) via the pull-down menu.
The Math / Science
The De Broglie equation is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. It was proposed by Louis de Broglie in 1924 and forms the basis of wave-particle duality, which states that every particle or quantum entity can exhibit both wave-like and particle-like properties.
The DeBrogile equation is:
where:
- λ is the DeBrogile wavelength
- h is Planck's Constant
- m particle mass
- v particle velocity
Note: m⋅v is momentum. So it is common to see this same formula in the following form:
where:
- λ is the DeBrogile wavelength
- h is Planck's Constant
- p is the momentum
De Broglie combined Einstein's famous energy equation, E = mc2, and Planck's equation, E = hv, to create this equation. The DeBrogile equation uses Planck's Constant (h = 6.626 x 10-34 m2*kg/s) to calculate the wavelength associated with an object relating to its momentum (p = mv).
Implications of the De Broglie Equation
Wave-Particle Duality:
According to the De Broglie hypothesis, particles such as electrons, protons, and even larger objects can exhibit wave-like properties. This means that they can be described by a wavelength, similar to light waves.
Quantum Mechanics Foundation:
The concept that particles have wavelengths is a cornerstone of quantum mechanics, leading to the development of quantum theories that describe the behavior of particles at the atomic and subatomic levels.
Electron Diffraction:
One of the key experimental verifications of the De Broglie hypothesis is electron diffraction. When electrons are fired at a crystal, they produce diffraction patterns similar to those produced by X-rays, indicating wave-like behavior.
Applications of the De Broglie Equation
Electron Microscopy:
The short De Broglie wavelength of electrons allows electron microscopes to achieve much higher resolution than light microscopes.
Quantum Mechanics and Chemistry:
The De Broglie wavelength concept is critical in understanding the behavior of electrons in atoms and molecules, leading to the development of quantum chemistry and the Schrödinger equation.
Particle Physics:
It plays a crucial role in particle physics, helping to explain the wave-like behavior of particles in high-energy physics experiments.
Example
Calculate the wavelength (in meters) of an electron traveling 1.24 x 107 m/s. The mass of an electron is 9.11 x 10-28 g.
Define variables:
- h = Planck's constant (6.626 x 10-34 m2*kg/s)
- m = 9.11 x 10-28 g = 9.11 x 10-31 kg
- v = 1.24 x 107 m/s
Substitute values into the De Broglie Equation:
λ = (6.626 x 10-34 m2*kg/s) / (9.11 x 10-31 kg) (1.24 x 107 m/s)
λ = 5.86 x 10-11m = 0.0586 nm
Energy, Photon and Wavelength Calculators
- Quantum Energy (E=h⋅v): Computes radiant energy in the Planck-Einstein relationship (E = h•ν) based on Planck's constant and a frequency of radiation.
- Energy of a Photon (E=h⋅f): Computes the energy of a photon based on the frequency and Planck's Constant.
- Photon Energy from Wavelength (E=(h⋅c)/λ): Computes the energy of a photon based on Planck's constant (h), the speed of light (c) and the wavelength of the photon ( λ)
- Photon Wavelength form Energy (λ=(h⋅c)/E): Computes the wavelength of a photon based on Planck's constant (h), the speed of light (c) and the energy of the photon (E).
- DeBroglie Wavelength (λ=h/(m⋅v)): Computes the wavelength of a particle based on the Planck's Constant and momentum (p = m•v).
- Plank Constant (h): Fundamental constant in physics that plays a central role in quantum mechanics which relates the energy of a photon to its frequency
Supplemental Material
ChemWiki (UCDavis) : De Broglie Equation (with example)
References
Whitten, et al. "Chemistry" 10th Edition. Pp. 144