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Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.The time that it takes for half of a sample to decay is known as the half life of the isotope.Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.

The key is to measure an isotope that has had time to decay a measurable amount, but not so much as to only leave a trace remaining.

Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.

Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.

The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.

This is consistent with the assumption that each decay event is independent and its chance does not vary over time.

The solution is: where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.

We can measure directly, for example by using a radiation detector, and obtain a good estimate of by analyzing the chemical composition of the sample.

The half-life , specific to each nuclide, can be accurately measured on a pure sample, and is known to be independent of the chemical composition of the sample, temperature and pressure.

Through analysis, a bone fragment is determined to contain 13% of its original carbon-14.

The half-life of carbon-14 is approximately 5,730 years. Since the quantity represents 13% (or 13/100ths) of , it follows that This is based on the decay of rubidium isotopes to strontium isotopes, and can be used to date rocks or to relate organisms to the rocks on which they formed.

• ###### Geologic Time Radiometric Time Scale

Jun 13, 2001. Most sedimentary rocks such as sandstone, limestone, and shale are related to the radiometric time scale by bracketing them within time zones that are determined by dating appropriately selected igneous rocks, as shown by a hypothetical example. Literally thousands of dated materials are now available.…

• ###### Radioactive dating anomalies -

Conflicting radioactive dating results are reported all the time and, on their own, there is no way of knowing what they mean. So geologists research how other geologists have interpreted the other rocks in the area in order to find out what sort of dates they would expect. Then they invent a story to explain the numbers as.…