An isotope is one of two or more atoms which have the same number of protons in their nuclei, but a different number of neutrons.
Radioisotopes are unstable isotopes: they spontaneously decay (emitting radiation in the process -- thus making them radioactive).
Recognizing this problem, scientists try to focus on rocks that do not contain the decay product originally.
For example, in uranium-lead dating, they use rocks containing zircon (Zr Si O Zircon and baddeleyite incorporate uranium atoms into their crystalline structure as substitutes for zirconium, but strongly reject lead.
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Radiometric dating is a method of determining the age of an artifact by assuming that on average decay rates have been constant (see below for the flaws in that assumption) and measuring the amount of radioactive decay that has occurred.
(This is consistent with the geologic 'age' assigned to the granites in which these zircons are found.) There is a significant amount of helium from that '1.5 billion years of decay' still inside the zircons.
Drawing any conclusions from the above depends, of course, on actually measuring the rate at which helium leaks out of zircons. The consistent answer: the helium does indeed seep out quickly over a wide range of temperatures.
This is what one of the recent RATE  papers reports on. In fact, the results show that because of all the helium still in the zircons, these crystals (and since this is Precambrian basement granite, by implication the whole earth) could not be older than between 4,000 and 14,000 years.
Radiometric Dating - A Brief Explanation Radiometric dating is the primary dating scheme employed by scientists to determine the age of the earth.
Radiometric dating techniques take advantage of the natural decay of radioisotopes.