  We can think of the nucleus of an atom as a sort of drop—a bunch of Some nuclides, both man-made and natural, are unstable, however. Their nuclei are in such violent turmoil that the nuclear forces cannot always hold them together, and various bits and pieces fly off. If we were to try to predict when one particular unstable nucleus would thus disintegrate, however, we could not succeed, because the instant any specific decay (or disintegration) event will occur is a matter of chance. Only if a large number of unstable nuclei of one kind are collected together can we say with certainty that, out of that number, a certain proportion will decay in a given time. It turns out that this proportion is the same regardless of any external conditions. This property of nuclei to decay by themselves is called radioactivity. Radioactive nuclei decay at constant rates regardless of temperature, pressure, chemical combination, or physical state. The process goes on no matter what happens to the atom. In other words, the activity inside the nucleus is in no way affected by what happens to the Most radioactive nuclides have rapid rates of decay (and lose their radioactivity in a few days, or a few years, at most); most of these are known today only because they are produced artificially. Some of them may have been present at the time the solar system was formed, but they have since decayed to such insignificant fractions of their original amounts that they can no longer be detected. Only a few radioactive nuclides decay slowly enough to have been preserved to this day, and so are present in nature. They are listed in Table II.
In a large number of radioactive nuclei of a given kind, a certain fraction will decay in a specific length of time. Let’s take this fraction as one-half and measure the time it takes for half the nuclei to decay. This time it is called the
In other words, after seven half-lives, less than 1% of the original amount of material will still be radioactive and the remaining 99%+ of its atoms will have been converted to atoms of another nuclide. This kind of process can be made the basis of a clock. It works, in effect, like the upper chamber of an hourglass. Mathematically it is written: N = N0e-?t
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 N0 = N + D where D = the number of daughter (decayed) atoms. We may then substitute into the first equation N = (N + D) e-?t and solve t = 1/? · 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.) 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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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