I'm just an undergrad who's interested in theoretical physics so please be gentle(adsbygoogle = window.adsbygoogle || []).push({});

I've always had the question in mind that does an electron possess a "rest frequency" that you could derive from it's rest energy... and since I didn't find any info on this on the net I decided to give a go to play with some equations.

Pardon me for not learning how to make the eqs with the code thingy:

E = mc^2

E = hf

so

hf = mc^2

and

f = mc^2 / h

This would be the "rest frequency" of the electron (or some other particle). I don't know if it is legimate to derive the (assumed) frequency this way. Now if we include the velocity of the particle we get

f = mc^2 / h√(1 - v^2 / c^2)

and because ,\ (lambda) = v / f, we get

,\ = v / mc^2 / h√(1 - v^2 / c^2)

= vh√(1 - v^2 / c^2) / mc^2

Now this is really funny: if the wavelenght of the particle is derived with this formula, the result is 100 times smaller than the result given by the de Broglie formula. [ ,\ = (h / p)√(1 - v^2 / c^2) ]

For example, if the speed of the electron is 0,1c, the formula I "proposed" gives the result

,\ = 2,41414856553*10^-13 m

and the de Broglie formula

,\ = 2,41414856553*10^-11 m

What goes wrong with my assumptions / formulas?

Does the electron even possess such a thing as "rest frequency"?

Btw. the other thing I find funny is that you can write the formula of the kinetic energy of the electron in the form

E_k = h(f - f_o), where f = the frequency of the electron at v and f_o = the rest frequency of the electron

Sorry if I ask/do stupid things, but I just want to know

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# What goes wrong here?

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