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## Homework Statement

Find the wavelength of an electron which is travelling at 4.35*10^6 m/s.

## Homework Equations

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

(9.109*10^-31)*(4.35*10^6)=(6.626*10^-34)*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.