The isotopic compostion fo rubidium is `.^(85)Rb-72` per cent and `.^(87)Rb-28` per cent. `.^(87)Rb` is weakly radioactive and decay by `beta^(-)` emission with a decay constant of `1.1xx10^(-11)` per year. A sample of the mineral pollucite was found to contain `450 mg Rb` and `0.72 mg` of `.^(87)Sr`. Estimiate the age of mineral pollution, starting any assumption made.

Explanation

`.^(85)Rb = 72%`
`.^(87)Rb = 28% overset(K = 1.1xx10^(-11)yr^(-1))(rarr) ``.^(87)Sr`
Sample contains `450 mg ``.^(87)Rb` and `0.72 mg .^(87)Sr`.
The average isotopic mass of `Rb`
`= (72xx85+28xx87)/(100) = 85.56`
Now `0.72 mg` of `Sr` is formed `Rb`, following `beta-` emision thus,
Mass of `.^(87)Rb` lost `= 0.72 mg`
Thus, initially the pollucite mineral contains
`Rb = 450 mg + 0.72 mg = 450.72 mg`
`.^(87)Rb` present of originally in it `= (28)/(100) xx 450.72`
`= 126.20 mg`
`.^(87)Rb` present at time `t = 126.20-0.72`
`= 125.48 mg`
Thus, `t = (2.303)/(1.1xx10^(-11))` log `(126.20)/(125.48)`
`= 5.202xx10^(8) yr`