De Broglie Equation

The De Broglie Equation calculator computes the wavelength based on the Planck's Constant and momentum (p = m•v).

INSTRUCTIONS: Choose units and enter the following:

• (m) Mass
• (v) 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 is:

   λ = h/(m·v)

where:

• λ is the DeBrogile wavelength
• h is Planck's Constant
• 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).

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