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Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left.After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.
The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.
All rocks and minerals contain long-lived radioactive elements that were incorporated into Earth when the Solar System formed.
These radioactive elements constitute independent clocks that allow geologists to determine the age of the rocks in which they occur.
The number of parent atoms originally present is simply the number present now plus the number of daughter atoms formed by the decay, both of which are quantities that can be measured.
Samples for dating are selected carefully to avoid those that are altered, contaminated, or disturbed by later heating or chemical events.