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Lesson_5.2b_Printable_PPT

Lesson_5.2b_Printable_PPT - Theory of Radioactivity The...

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The rate of disintegration of a radioactive material is proportional to the number of radioactive atoms present at that time. If we start with N o number of radioactive atoms of a substance, after an interval of time t, if N is the number of atoms remaining of the original substance, then a relation λ is a constant and is called the decay constant of the material. Theory of Radioactivity N t t λ = - N = N o e - λ t between N and N o can be written as The atoms of the original material are called parent atoms and the atoms that are disintegrated are called the atoms of daughter element.
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Half-life of a Radioactive Element The time taken for half the original number of radioactive atoms in a sample to disintegrate is called the half-life period of that material, represented by T . The value of N will be exactly half of N o in one half-life period T. When t = T, N/N o = ½ N = N o e - λ t ½ = e - λ T Taking ln of both sides gives Ln( ½ ) = - λ T 0.693 = - λ T 0.693 T λ = 0.693 T λ = 0.693 ( ) t T o N t N e - =
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If r o is the initial activity of a sample of radioactive material and r n is the activity after n half lives, then a relation between r n and r o can be written as If A o is the amount of radioactive substance in the beginning, after one half-life T , 1 2 n n o r r = there will be A o /2 left.
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