Physics/Frequency of electrons
QUESTION: Can electrons to have a frequency below the thz range?
ANSWER: Depends what you mean by the "frequency" of an electron.
Electrons can be described as DeBroglie Waves, and these waves do have a frequency. However, the frequency of these waves have no measurable effects; so scientists invariably discuss the wavelength of a DeBroglie Wave, which does have measurable effects.
The formula for the frequency ƒ of a DeBroglie wave
is given by
ƒ = γ m(0)c^2/h
where γ is 1/sqrt(1 - v^2/c^2)
m(0) is the rest mass of the object, v is its velocity, c is the speed of light, and h is Planck's Constant (PC).
The rest mass of an electron times the speed of light squared is about 5 x 10^5 eV,
and PC is about 4 x 10^-15 eV-sec
Thus, an electron with velocity far below c will have f on the order of 10^20 Hz
As the electron velocity gets closer c, note that f increases. Thus, it would not be possible for an electron's DeBroglie Wave to have f less than 10^20 Hz
On the other had, if you mean can an electron vibrate more slowly than 1 tHz, that is actually very easy to calculate. Just figure what type of electro-magnetic radiation has a frequency of 1 tHz, and then check if EM radiation has a lower frequency than that. If EM radiation exists with a lower frequency than that, then an electron can do so. I'll leave it to you to find if EM radiation exists with a frequency lower than 1 tHz
---------- FOLLOW-UP ----------
QUESTION: I understand, both IR Waves and microwaves have frequencies below thz. My followup question is, is it the vibrational frequency of electrons that interfere in the double slit experiments or the deBroglie wave frequency? Also, is it the vibrational frequency or the debroglie wave frequency that governs the electrons spin?
> is it the vibrational frequency of electrons that interfere
> in the double slit experiments
> or the deBroglie wave frequency?
I tried to make it clear in my first response, but now I will make it very explicit: do NOT mention the DeBroglie FREQUENCY. It is, for any useful definition of the term, a meaningless value.
I hope you understand that it is not the frequency of light waves that directly result in an interference pattern when you have EM waves going through a slit, it is the WAVELENGTH of these EM waves that results in these patterns.
In the same way, electrons create an interference pattern because of the DeBroglie WAVELENGTH -- the frequency has NOTHING to do with the pattern.
Also, please note that electrons have a vibrational frequency only if they are in a vibrating electric field (E-field). Otherwise the expectation value for their vibrational frequency is zero -- which is the quantum mechanical equivalent of stating that they have no vibrations.
> is it the vibrational frequency or the debroglie wave frequency
> that governs the electrons spin?
Neither. An electron's spin is an intrinsic quantity of an electron's existence, in the same way that each electron has its charge. All electrons have the same amount of spin, whether they or not they are in a vibrating E-field (and thus vibrating themselves), and whether or not they are moving (and thus have a DeBroglie Wavelength).