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Define half life period of a radioactive sample. Arrive at the relation between half life and decay constnat. |
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Answer» SOLUTION :It is the TIME during which half of the atoms of radioactive substance UNDERGO disintegration Consider the relation, `N=N_(0)e^(-lambda t)…(1)` Where `N_(0)` = initial number of atoms in a radioactive substance. N=Number of atoms at GIVEN instant t. `lambda` = Decay CONSTANT. For half life period `t=T_((1)/(2))` and `N=(N_(0))/(2)` `(1)implies(N_(0))/(2)=N_(0)e^(-lambda T_((1)/(2)))` `(N_(0))/(2)=(N_(0))/(e^(lambda T_((1)/(2)))` `lambda T_((1)/(2))=log_(e)2""[because e^(x)=yimpliesx=log_(e)(y)]`, `lambdaT_((1)/(2))=2.303log_(10)(2)` `lambda T_((1)/(2))=2.303xx0.3010` `T_((1)/(2))=(0.693)/(lambda)` |
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