1.

.^(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?

Answer» <html><body><p></p>Solution :We know, <br/> `lambda_(av) = (0.693)/(<a href="https://interviewquestions.tuteehub.com/tag/22-294057" style="font-weight:bold;" target="_blank" title="Click to know more about 22">22</a>) = <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>.15xx10^(-2) "year"^(-1)` <br/> For the decay involving <a href="https://interviewquestions.tuteehub.com/tag/two-714195" style="font-weight:bold;" target="_blank" title="Click to know more about TWO">TWO</a> <a href="https://interviewquestions.tuteehub.com/tag/parallel-1146369" style="font-weight:bold;" target="_blank" title="Click to know more about PARALLEL">PARALLEL</a> paths,<br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/DPB_PHY_CHM_IX_C04_E01_050_S01.png" width="80%"/> <br/> We have `lambda_(<a href="https://interviewquestions.tuteehub.com/tag/ac-361271" style="font-weight:bold;" target="_blank" title="Click to know more about AC">AC</a>) = lambda_("Th path") + lambda_("Fr path")` <br/> `:. Lambda_(Ac) xx "Fraction of Th" = lambda_("Th path")` ....(1) <br/> `lambda_(AC) xx "Fraction of Fr" = lambda_("Fr path")` .....(2) <br/> or `lambda_(AC) xx (1 - "Fraction of Th") = lambda_("Fr path")` .....(3) <br/>Thus by eqs. (1) and (3) we get <br/> `lambda_(AC) =lambda_("Th path") + lambda_("Fr path")` <br/> Thus by eqs. (1) and (3) we get <br/> `lambda_(AC) = lambda_("Th path")+ lambda_("Fr path")` <br/>Thus, Fractionlal yield of `Th = (lambda_("Th path"))/(lambda_("Ac path"))` <br/> or `lambda_("Th path")=3.15xx10^(-2)xx(2)/(100)` <br/> `=6.30xx10^(-4)yr^(-1)` <br/> Also Fractional yeild of Fr`=(lambda_("Fr path"))/(lambda_(Ac path))` <br/> `:. lambda_(Fr) = 3.15xx10^(-2) xx (98)/(100) =3.087xx10^(-2) yr^(-1)`</body></html>


Discussion

No Comment Found

Related InterviewSolutions