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Decay of nuclei is a completely random process, and you really don't want to use it to define a time-scale.

What you had in mind is the SI-definition of the second, which reads (http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.ht...):

  """
     The second is the duration of 9 192 631 770 periods
     of the radiation corresponding to the transition
     between the two hyperfine levels of the ground state
     of the caesium 133 atom.
  """
The details of this effect are a little more complicated, but it boils down to the fact that you can measure the "angular momentum" of your nuclei when you have them pass through a non-uniform magnetic field. Particles in the one state are deflected differently than particles in the other state. And when you irradiate a particle beam in the F=0 state with the right frequency (9.2 GHz) you can very efficiently swap many particles over to the F=1 state. By adjusting your frequency sufficiently to find the maximum rate of flips, you can can tune for the exact 9'192'631'770 Hz.

The cesium particles have not decayed, in principle you could run forever on a certain supply of atoms... even though in practice a Cs-beam is produced on one side, at a hot filament, and dumped to the other side of the clock after passed through the apparatus that performs the steps described above. They will be disposed of when the lifetime of the beam-tube is reached (typically 10 years or so with a few grams of cesium inside).



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