Consider ""^(224)Ra overset(-alpha)rarr ""^(220)Rn overset(-alpha) ""^(216)Po where t_((1)/(2)) (Ra)= 3.64 yr, t_((1)/(2)) (Rn)= 55s. Determine the N (Ra)/N (Rn) ratio once secular equilibrium in which t_((1)/(2)) (parent) gt gt t_((1)/(2)) (daughter) or lamda (parent) lt lt lamda (daughter) has been established.

Consider ""^(224)Ra overset(-alpha)rarr ""^(220)Rn overset(-alpha) ""^

1.	Consider ""^(224)Ra overset(-alpha)rarr ""^(220)Rn overset(-alpha) ""^(216)Po where t_((1)/(2)) (Ra)= 3.64 yr, t_((1)/(2)) (Rn)= 55s. Determine the N (Ra)/N (Rn) ratio once secular equilibrium in which t_((1)/(2)) (parent) gt gt t_((1)/(2)) (daughter) or lamda (parent) lt lt lamda (daughter) has been established.
Answer» Solution :We have, `(N_(1))/(N_(2))= (lamda_(2))/(lamda_(1))` Now, `lamda_(1)= (0.6932)/((t_((1)/(2)))_(1))= (0.6932)/(3.64 xx 60 xx 60)= 2.20 xx 10^(-6) s^(-1)` `lamda_(2)= (0.6932)/((t_((1)/(2)))_(2))= (0.6932)/(55)= 1.26 xx 10^(-2) s^(-1)` THUS, `(N(Ra))/(N(RN))=(1.26 xx 10^(-2))/(2.20 xx 10^(-6))=5727`