""^(227)Ac has a half-life of 21.8 years with respect to radioactive decay. The decay follows two parallel paths, one leading to ""^(227)Th and the other leading to ""^(223)Fr. The percentage yields of these two daughter nuclides are 1.2% and 98.8% respectively. what is the rate constant in y^(-1), for each of the separate paths?

""^(227)Ac has a half-life of 21.8 years with respect to radioactive d

1.	""^(227)Ac has a half-life of 21.8 years with respect to radioactive decay. The decay follows two parallel paths, one leading to ""^(227)Th and the other leading to ""^(223)Fr. The percentage yields of these two daughter nuclides are 1.2% and 98.8% respectively. what is the rate constant in y^(-1), for each of the separate paths?
Answer» Solution :We have, `lamda_(Ac)= (0.6932)/(t_((1)/(2)))= (0.6932)/(21.8)= 3.18 xx 10^(-2) yr^(-1)` `lamda_(TH)=` (FRACTIONAL yields of Th) `xx lamda_(Ac)` `=(1.2)/(100) xx 3.18 xx 10^(-2) = 3.8 xx 10^(-4)yr^(-1)` SIMILARLY, `lamda_(FR)= (98.8)/(100) xx 3.18 xx 10^(-2)= 3.14 xx 10^(-2) yr^(-1)`