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The technique of comparing the abundance ratio of a radioactive isotope to a reference isotope to determine the age of a material is called radioactive dating.Many isotopes have been studied, probing a wide range of time scales.

(For some nuclides which decay by the process of electron capture, such as Beryllium-7, Strontium-85, and Zirconium-89, the decay rate may be slightly affected by local electron density, therefore these isotopes may not be as suitable for radiometric dating.) But in general, the half-life of any nuclide is essentially a constant.In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter.Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years (e.g., tritium) to over 100 billion years (e.g., Samarium-147).Additionally, elements may 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. That is, at some point in time, an atom of such a nuclide will spontaneously transform into a different nuclide.The boat of a pharaoh was discovered in a sealed crypt and reassembled in a museum near the pyramids (see Fig. The age of our galaxy and earth also can be estimated using radioactive dating.Using the decays of uranium and thorium, our galaxy has been found to be between 10 and 20 billion years old and the earth has been found to be 4.6 billion years old. Within experimental error, this estimate agrees with the 15 billion year estimate of the age of the Universe.This transformation may be accomplished in a number of different ways, including radioactive decay, either by emission of particles (usually electrons (beta decay), positrons or alpha particles) or by spontaneous fission, and electron capture.While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques.The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate.This normally involves isotope ratio mass spectrometry.

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With the ship on dry land and its rocking motion gone, Natsu regains his vitality and confronts "Salamander," declaring himself to be a member of Fairy Tail, thereby exposing the Mage as an impostor.