In natue a decay chain sereis starts with ._(90)h^(232) and finally terminates at ._(82)Pb^(208). A throium ore sample was found to contain 8xx10^(-5) mL of He At STP and 5xx10^(7)g of Th^(232). Find the age of ore sample assuming that sourcesof He to be only due to decay of Th^(232) Also assumecomplete retention of He within the ore, t_(1//2) for Th^(232) = 1.39xx10^(10) year.

In natue a decay chain sereis starts with ._(90)h^(232) and finally te

1.	In natue a decay chain sereis starts with ._(90)h^(232) and finally terminates at ._(82)Pb^(208). A throium ore sample was found to contain 8xx10^(-5) mL of He At STP and 5xx10^(7)g of Th^(232). Find the age of ore sample assuming that sourcesof He to be only due to decay of Th^(232) Also assumecomplete retention of He within the ore, t_(1//2) for Th^(232) = 1.39xx10^(10) year.
Answer» Solution :We KNOW, `._(90)Th^(232) rarr ``._(82)Pb^(208) + 6 ``._(2)He^(4) + 4 ``._(-1)e^(0)` `:' 6xx22400 mL` He is formed by `232g Th` decay `:. 8xx10^(-5) mL` He is formed by `= (232xx8xx10^(-5))/(6xx22400)g Th` decay `= 1.38xx10^(-7)g Th` decay At `t = t`, sample has `Th = 5xx10^(-7) g prop N` At `t = 0`, sample has `Th = 5xx10^(-7) + 1.385 xx 10^(-7) prop N_(0) = 6.38xx10^(-7)g` For `Th` decay `:' t = (2.303)/(LAMBDA) log_(10) (N_(0))/(N)` `= (2.303xx1.39xx10^(10))/(0.693) log_(10) (6.38xx10^(-7))/(5x10^(-7))` `=4.89xx10^(9)` year