Calculating De Broglie Wavelength from Kinetic Energy

[jinksys]

Homework Statement

Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by

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

Homework Equations

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.

 

[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.