In a sample of pitchblende the ratio of ""^(206)Pb, ""^(238)U= 0.2: 1 by weight. If the disintegration constant of ""^(238)U " is " 1.54 xx 10^(-10) per year and all Pb is supposed to be originated from uranium, what will be the age of the mineral?

In a sample of pitchblende the ratio of ""^(206)Pb, ""^(238)U= 0.2: 1

1.	In a sample of pitchblende the ratio of ""^(206)Pb, ""^(238)U= 0.2: 1 by weight. If the disintegration constant of ""^(238)U " is " 1.54 xx 10^(-10) per year and all Pb is supposed to be originated from uranium, what will be the age of the mineral?
Answer» SOLUTION :INITIAL moles: `N^(0)""^(238)U rarr ""^(206)PB` Moles after time `t: (N^(0)-x) " " x` `(WT. "of " ""^(206)Pb)/("wt. of" ""^(238)U)= (0.2)/(1)` `therefore ("mole of" Pb^(206))/("mole of " U^(238))=(0.2//206)/(1//238)= (0.231)/(1)` or `(x)/(N^(0)-x)= 0.231` Adding 1 in both sides, `1+ (x)/(N^(0)-x)= 0.231 +1` `(N^(0))/(N^(0)-x)= 1.231` We have, `lamda= (2.303)/(t) "log" (N^(0))/(N)` or `lamda= (2.303)/(t)"log" (N^(0))/(N^(0)-x)` `1.54 xx 10^(-10) = (2.303)/(t) "log" 1.231` `t= 1.35 xx 10^(9)` years