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.^(227)Ac has a half-line of 22 year with respect to radiioactive decay. The decay follows two parallel paths, one leading to .^(227)Th and the other leading to .^(223)Fr. The percentage yiedls of these two daughter nuclides are 2% and 98.0% respectovely. What is the rate constant in "year"^(-1), for each of the separate paths? |
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Answer» Solution :We know, `lambda_(av) = (0.693)/(22) = 3.15xx10^(-2) "year"^(-1)` For the decay involving TWO PARALLEL paths,  We have `lambda_(AC) = lambda_("Th path") + lambda_("Fr path")` `:. Lambda_(Ac) xx "Fraction of Th" = lambda_("Th path")` ....(1) `lambda_(AC) xx "Fraction of Fr" = lambda_("Fr path")` .....(2) or `lambda_(AC) xx (1 - "Fraction of Th") = lambda_("Fr path")` .....(3) Thus by eqs. (1) and (3) we get `lambda_(AC) =lambda_("Th path") + lambda_("Fr path")` Thus by eqs. (1) and (3) we get `lambda_(AC) = lambda_("Th path")+ lambda_("Fr path")` Thus, Fractionlal yield of `Th = (lambda_("Th path"))/(lambda_("Ac path"))` or `lambda_("Th path")=3.15xx10^(-2)xx(2)/(100)` `=6.30xx10^(-4)yr^(-1)` Also Fractional yeild of Fr`=(lambda_("Fr path"))/(lambda_(Ac path))` `:. lambda_(Fr) = 3.15xx10^(-2) xx (98)/(100) =3.087xx10^(-2) yr^(-1)` |
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