Essay About Radioactive Decay And 693.02Lnl L

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Radioactive DecayRadioactive Decayv Dynamic , or time-varying, properties of nuclei: Ø Discovery of the radioactivity by Henri Becquerel in 1896.§ radioactive decay and § nuclear reaction. o Discovered the radioactivity of Uranium whileinvestigating the fluorescence properties of Uranium salts.Ø Both characterized by:· Transition from some initial system to some final system, occurring either:o spontaneously (radioactive Decay) or Ø Discovery of two more radioactive elements: Poloniumo artificially (nuclear reaction) and Radium by Pierre & Marie Curie, 1898.v Radioactive decay: the nucleus of an atom Ø Discovery of more radioactive elements: Thorium,· emits: Actinium, Radiothorium, , in a few years.o an alpha particle, o a beta particle, o a gamma ray Ø Today hundreds of radioactive isotopes of different· Or capture: elements are known.o an electron from an extra-nuclear shellØ Man-made radioactive element (30P) by Irene Curie &v parent: the initial radioactive nuclide in any decay mode Pierre Joliot, 1934v daughter: the product nuclidev radioactive decay chain: several successive radioactivegeneration.12The Radioactive Decay law:Assume:Ø N radioactive nucleiØ At time tThe number dN decaying in a time dt is proportional to N :Nhalf-life,t 21: the time necessary for half of the nuclei todecay§ put NN =02t21== 693.02lnl l mean lifetime, t : the average time before a nucleus decaysl-= ( dtdN ) where: l o disintegration or decay constant.lØ rhs of the equation is the probability per unit time forthe decay of an atom.Ø The Probability of decay is CONSTANT, regardlessof the age.Integrating the decay constant equation gives the exponential law of radioactive decay:l dNdtN = ò l dtN = ò dN eNtN = – l t 0t=ò ò 0 0 ¥¥dtdtdNtdtdtdN= 1t = 2ln t21 =Þ t21693.02ln t = t The number of decays between t and ( tΔ ) :=D+-=DeNttNtNN )()(0 – l t 1( – e – l t ) Iftt<, then we can say:=D teNN l0 - l t D )(tNNo=o )0( dN dt=l eN - l t 34dn=)eAtNA ol = 0 Then we can define the activity A: (sincedtlN)( - l t where:tAA 0l=== )0( N 0 Ø Measuring the number of counts NΔ in a timeinterval tD gives the activity of the sample only if > 21 (Secular equilibrium)