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Define radioactive decay constant and half-life and derive a relation between them. |
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Answer» Decay constant i.e. `-(dN)/(dt) prop N_(0)` Decay constant is defined as the TIME after which the number of radioactive atoms reduce to 1/e times the original number ofatoms. Relation between half LIFE T and `lambda`. Half-life period The half-life of a radioactive substance is defined as the time during which half of the atoms of radioactive substancewill disintegrate. Let us denote the half-time of a substance by T. Then, by definition, after time T, number of atoms left behind will be `(N_(0))/(2)`. ...(1) Setting this CONDITION i.e. when `t=T, N=(N_(0))/(2)` in the given equation (1), we GET `(N_(0))/(2)=N_(0)e^(-lambda T)` or `e^(-lambdaT)=1/2 ` or `e^(lambdaT)=2` or `lambda T=log_(e)2=2.303 log_(10)2` `=2.303 xx 0.3010=0.693` Therefore, `T=(0.693)/(lambda)` ...(2) Thus, half life of radioactive substance is inversely proportional to its decay constant and is a characteristic property of its nucleus and cannot be altered by any known method. |
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