I understand that photon's energy equal hf, but why electon's also?

[td21]

Homework Statement

Photon:E=hf
Electron:E=hf? where f is the frequency of the matter wave.
But where does the rest mass energy of electron goes, does it include in the "hf"?

Homework Equations

The Attempt at a Solution

I think the "f" of photon is different from the "f" of electron.
"f" of photon is exactly the light wave frequency(can be observed), while the "f" of electrons is the "matter wave"'s.
For everything such as Car, the energy is also "hf", where "f" of the car is the matter wave frequency of the car.
So for everything with mass, the "hf" energy also includes any energy such as rest mass, kinetic, potential, and so on. It's because all energy is reflected by the frequency of matter wave. And photon is a special case as it has no mass.

 

[td21]

can somebody help please i have upload attachment for further.

 

[td21]

Further elaboration:
I think E=hf holds for electron when the energy of electron is much GREATER than its rest energy.
My proof:
$E^2=p^{2}c^{2}+E_o^2$
When $E>>>E_0$,
$E^2=p^{2}c^{2}$
leads to
$E=pc$

By de Broglie wavelength:
$p=\frac{h}{\lambda}$

Combine:
$E=\frac{hc}{\lambda}$
so
$E=hf$!Is my work correct? Or electron's energy is equal to "hf" all the time even when its comparable to rest mass energy?
Thanks.

 

[td21]

However i find that even some use E=hf for electron moving with momentum with only 10^-25, which means KE only 10^-19? so KE is very small and rest mass energy dominates, why still use E=hf??