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 sources of `He` to be only due to decay of `Th^(232)` Also assume complete retention of `He` within the ore, `t_(1//2)` for `Th^(232) = 1.39xx10^(10)` year.

Explanation

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