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Elements exist in different isotopes , with each isotope of an element differing in the number of neutrons in the nucleus. A particular isotope of a particular element is called a nuclide. Some nuclides are naturally unstable. That is, at some point in time, an atom of such a nuclide will spontaneously change into a different nuclide by radioactive decay. The decay may happen by emission of particles usually electrons beta decay , positrons or alpha particles or by spontaneous nuclear fission , and electron capture. The age is calculated from the slope of the isochron line and the original composition from the intercept of the isochron with the y-axis.

The discovery of the radioactive properties of uranium in by Henri Becquerel subsequently revolutionized the way scientists measured the age of artifacts and supported the theory that Earth was considerably older than what some scientists believed. However, one of the most widely used and accepted method is radioactive dating. All radioactive dating is based on the fact that a radioactive substance, through its characteristic disintegration, eventually transmutes into a stable nuclide. When the rate of decay of a radioactive substance is known, the age of a specimen can be determined from the relative proportions of the remaining radioactive material and the product of its decay.

These radioactive isotopes are unstable, decaying over time at a predictable rate. As the isotopes decay, they give off particles from their nucleus and become a different isotope. The parent isotope is the original unstable isotope, and daughter isotopes are the stable product of the decay. Half-life is the amount of time it takes for half of the parent isotopes to decay. The decay occurs on a logarithmic scale.

Measurement of N, the number of 14 C atoms currently in the sample, allows the calculation of t, the age of the sample, using the equation above. The above calculations make several assumptions, such as that the level of 14 C in the atmosphere has remained constant over time. The calculations involve several steps and include an intermediate value called the "radiocarbon age", which is the age in "radiocarbon years" of the sample: Radiocarbon ages are still calculated using this half-life, and are known as "Conventional Radiocarbon Age". Since the calibration curve IntCal also reports past atmospheric 14 C concentration using this conventional age, any conventional ages calibrated against the IntCal curve will produce a correct calibrated age.

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