and solve
t = 1/λ · ln(1 + D/N)
where ln = the natural logarithm, the logarithm to base e.
This kind of system can be represented crudely by an old-fashioned
hourglass, as shown in the figure, which has the parameters of these
equations marked. (Keep in mind, however, that this is only a gross
analogy. Nuclear clocks run at logarithmically decreasing rates, but the
speed of a good hourglass is roughly constant.)
[Illustration: _An hourglass illustrates an ideal closed system. Nothing
is added and nothing is removed—the sand just runs from the top bulb to
the bottom._]
Remember that the decaying nucleus does not disappear. It changes into
another nucleus, and this new nucleus forms an atom that may be captured
and held fixed by natural processes. The decayed nuclei are thus
collected, so that here we have the bottom chamber of the hourglass.
But sometimes we need only the top chamber of an hourglass.