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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.

, 1830s; (ENIAC, Electronic Numerical Integrator and Calculator, first all-electronic, completed) John Presper Eckert, Jr., John Mauchly, U.

S., 1945; (dedicated at University of Pennsylvania) 1946; (UNIVAC, Universal Automatic Computer, handled both numeric and alphabetic data) 1951; (personal computer) Steve Wozniak, U.

S., 1903; (neon lamp) Georges Claude, France, 1911; (tungsten filament) Irving Langmuir, France, 1889; (Celanese) Henry and Camille Dreyfuss, U. van Musschenbroek, University of Leyden, Holland, 1746, from where name originated.(limited to one-mile range) Christian Hulsmeyer, Germany, 1904; (pulse modulation, used for measuring height of ionosphere) Gregory Breit, Merle Tuve, U.

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.S., 1976.(geographer who pieced together continents into a single landmass on maps) Antonio Snider-Pellegrini, France, 1858; (first proposed in lecture) Frank Taylor, U. 1912; (first comprehensive detailed theory) Alfred Wegener, U.

S., 1879; (first widely marketed incandescent lamp) Thomas A. S., 1879; (mercury vapor lamp) Peter Cooper Hewitt, U. von Kleist of Kamin, Pomerania, 1745; independently evolved by Cunaeus and P. S., 1926; (first all-electric television image) Philo T.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.

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