De Broglie Wavelength

Question 1.

            Derive the equation λ=h/p starting with the results of the photoelectric effect and the relativistic equation E_photon= c*p. 

The resulting equation of the photoelectric effect is E = h*f.  Meaning that as the frequency of a wave increases the energy also increases since the h is a constant.

The relativistic equation, E_photon= c*p, deals with the speed of light and linear momentum of a photon. 

If we start by setting the photoelectric equation and relativistic equation equal:

h*f = c * p

Then if we divide both sides by p:

(h*f) / p = c

Now divide both sides by f:

h / p = c / f

Since we already know that:

λ = c / f

Simply substitute this in and we get the equation:

λ = h / p