# What do the Broglie equations relate?

Aug 2, 2014

The de Broglie equations relate (a) the wavelength λ to the momentum $p$ and (b) the frequency $f$ to the total energy $E$.

You can find the equations at What is the De Broglie equation?

Equation 1 is

λ = h/p = h/(mv)

It enables us to calculate the wavelength of a particle if we know its mass and velocity.

EXAMPLE

Calculate the wavelength of an electron with a speed of 3.00 × 10⁷ m/s.

Solution

λ = h/p = h/(mv) = (6.626 × 10⁻³⁴"kg·m²s⁻¹")/(9.11 × 10⁻³¹"kg" × 3.00 × 10⁷"m·s⁻¹") = 2.42 × 10⁻¹¹ m = 24.2 pm

Equation 2 is

$f = \frac{E}{h}$

Since fλ = v,

v/λ = E/h

or

E = (hv)/λ

Example

What is the energy of the electron in the above example?

Solution

E = (hv)/λ = ( 6.626 × 10⁻³⁴"J·s" × 3.00 × 10⁷"m·s⁻¹")/(2.42 × 10⁻¹¹"m") = 8.20 × 10⁻¹⁶ J