where
N = the number of radioactive atoms present in the system now,
N₀ = the number that was present when t = 0, (in other words, at the
time the clock started),
e = the base of natural (or Napierian[8]) logarithms (the numerical
value of e = 2.718 ...),
λ (lambda) = the decay rate of the radioactive material, expressed
in atoms decaying per atom per unit of time,
t = the time that has elapsed since the origin of system, expressed
in the same units.
Obviously, in ordinary computations that would not be enough information
to calculate the time, because there still are two unknowns, _N₀_ and
_t_. In a closed system, however, the atoms that have decayed do not
disappear into thin air. They merely change into other atoms, called
daughter atoms, and remain in the system.
And at any point in time, there will be both PARENT and DAUGHTER atoms
mixed together in the material. The older the material, the more
daughters and the fewer parents. Some daughters are also radioactive,
but this does not change the basic situation. Thus it follows that