Find the wavelength of an electron which is travelling at 4.35*10^6 m/s.
p = h/λ
p = mv
E = hf
E = 1/2mv^2
The Attempt at a Solution
I know this can be easily solved using the momentum equation and De Broglie's law like this:
mv = h/λ
λ ≈ 0.167nm
But here comes the actual question...
Why can't I solve this with the second law E = hf and the classical 1/2mv^2?
1/2mv^2 = hf, where f = (c/λ)
This gives me an incorrect result. If I wanted to use kinetic energy, I would have to first convert it to momentum
p = √(2Em), which I would use with p = h/λ.
After all, for instance the photoelectric effect can be calculated using kinetic energy with hf-W.
I think I've missed something relevant, and I can't seem to find the answer. Sorry if this is too obvious.