You're just about there. A Joule is a kg-m^2/s^2, so what your formulas
says is that the frequency in Hz or inverse seconds is 1.36x10^50 x
mass, where mass is given in kg.
Now you can figure out the frequency of a carbon 12 atom,
remembering that atomic mass of 12 means that one mole (6x10^23 atoms)
has mass of 12 gm, so one atom has mass of 2x 10^-23 gm, or 2x 10^-26
kg. I get a frequency of 2.72 x10^24 Hz.
Of course you may wonder what in the world we are talking about
here- what's the 'frequency' of an atom? It's really a quantum
mechanical property. Quantum mechanics allows systems to exist in a
mixture of different states, all at the same time. If a system is
prepared so that it is in a mixture of two different states with
different frequencies, then some of the properties of the system will
oscillate with a frequency that's the difference of the frequencies of
the two ingredient states. The common name for this is "beat
An example of this from particle physics is neutrino oscillation.
Neutrinos come in three types, or "flavors" -- electron, muon, and tau.
These we now know to have small masses which are different from each
other. These small masses correspond to different frequencies according
to your formula above. Neutrinos are made as an electron neutrino, a
muon neutrino, or a tau neutrino, but these three states are mixtures
of the states with definite mass, and so the neutrinos slowly oscillate
from one flavor to another and back again as they travel through space.
Measurements of this oscillation rate gives us indications about the
differences of the masses of the neutrinos.
Mike W. (and Tom)
(republished on 07/21/06)