There really is not a frequency for matter.  However, there are two phenomena you can consider to be similar: thermal vibrations and the DeBroglie wavelength. 

 

Thermal vibrations arise from any matter in an environment that is not at absolute zero temperature.  The atoms and molecules can interact with the energy stored in the heat of the environment.  The energy from temperature is studied in of thermodynamics and statistical mechanics. 

 

In general, the each degree of freedom of a particle can be described as having ½ * k * T worth of energy:

 

Energy = ½ * k * T per degree of freedom

 

where k is Boltzmann’s constant and T is the temperature measured relative to absolute zero (typically T is measured in degrees Kelvin).   Examples of this can be seen in the derivation of heat capacity, the velocity distribution of gas molecules (Maxwell-Boltzmann Distribution), the Ideal Gas Law, and several other incidents.

 

 

The DeBroglie Wavelength usually associated with massive particles like electrons, but can be used to determine if quantum mechanics is important in a problem.  Basically, if the DeBroglie Wavelength is bigger or comparable to some characteristic size of the situation, then quantum mechanics or wave mechanics must be considered.   If the DeBroglie Wavelength is much small than some characteristic length, then the situation can be appropriately described using classical or relativistic formulation.

 

Check out the webpage Wave nature of electron for more detailed information.   I will cut the chase on the details of his derivation

 

The cool thing DeBroglie (Prince Louis de Broglie) did was to figure that if photons of light could act like waves or particles, then perhaps something could be done with considering massive particles as waves.   This simple idea, with amazing application and implication, led to DeBroglie receiving the Nobel Prize in 1929.

 

What he did was to start from the energy and momentum equations for photons:

 

Energy_photon = h * frequency = h * c / wavelength,

 

Momentum _photon = h / wavelength (note this is just the magnitude)

 

where h is Planck's constant and c is the speed of light, and the wavelength is wavelength of the photon’s oscillation.

 

The he considered the equation for the momentum of an object with mass:

 

Momentum_{massive object} = mass * speed (note this is just the magnitude).

 

Combining these two equations for a massive object yields:

 

mass * speed = h / wavelength

 

or

 

wavelength = h /(mass * speed).

 

For example, everyday items such as cars or balls traveling a couple tens of miles per hour, the DeBroglie wavelength works out to be much less than the diameter of a nucleus (DeBroglie wavelength 10^-34 to 10^-38 meters versus nuclear diameter 10^-14 m).   So the car or baseball should be treated as a particle.

 

As another example, for electrons in an accelerator (something like moving at .33 times the speed of light, ignoring relativistic effects), the DeBroglie wavelength is on the order of 10^-12 m which is about 100 times smaller than the size of an atom, so quantum mechanics is still not terribly important in the collision mechanics, but it can be important in the particle formation after the collision.  So the electrons should be treated as particles not as waves.

 

And finally, for electrons in electron diffraction scattering experiment accelerated by 100 Volts resulting in a speed of something like 6 x 10⁶ m/s then the DeBroglie wavelength is on the order of 10^-11 m, which is the same order of magnitude as bond lengths, so the electrons act like waves.

 

Sincerely,

 

Tom “Jiggly King” Cull