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.

The isotopic compostion fo rubidium is .^(85)Rb-72 per cent and .^(87)

1.	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.
Answer» Solution :`.^(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`