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The De Broglie Equation (relativistic) calculator computes the wavelength based on the Planck's Constant and momentum (p = m•v). This form of the equation takes into account the relativistic effect of high velocities.
INSTRUCTIONS: Choose units and enter the following:
- (m) This is the mass
- (v) This is the velocity
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 DeBrogile equation (relativistic)is:
`λ = h/(m·v) · sqrt(1 - v^2 / c^2`
where:
- λ is the DeBrogile relativistic wavelength
- h is Planck's Constant
- c is the Speed of Light
- m is the mass
- v is the velocity
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).
Reference
- Special thanks to Viktor T. Toth for describing this formula on Quora.
