Derivation of De Broglie wavelength

[PhiJ]

The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ

But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.

 

[Hans de Vries]

The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ
But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.

It only works if you take: wave-speed = [itex]\frac{c^2}{v}[/tex] where v is the physical<br /> speed of the electron, this is however an ad-hoc assumption here. It's not<br /> that hard to derive λ=h/ρ directly from E=hf but it takes Special Relativity:<br /> <br /> <a href="http://www.chip-architect.com/physics/deBroglie.pdf" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://www.chip-architect.com/physics/deBroglie.pdf</a>Regards, Hans[/itex]