# De Broglie Wavelength

1. Sep 19, 2010

### jinksys

1. The problem statement, all variables and given/known data
Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by

$$\lambda = \frac{hc}{\sqrt{KE(KE + 2mc^2)}}$$

2. Relevant equations

3. The attempt at a solution
I know:

$$KE = {\gamma}mc^2 - mc^2 = pc - mc^2$$

But from here I am lost. I have a hunch that I need to use the equation that equates Energy and Momentum, but I'm lost.

Last edited: Sep 19, 2010
2. Sep 19, 2010

### zhermes

The problem is that your equation only applies to the relativistic limit, in general
$$E_k = \sqrt{(pc)^2 + (mc^2)^2} - mc^2$$
Try using that.