The isotopic composition of rubidium is `Rb^(85):73%` and `Rb^(87):28%Rb^(87)` is weakly radioactive and decay by `beta^(c-)-` emission with a decay constant of `1.1xx10^(-11) ` per year. A sample of the mineral pollucite was found to contain `450g Rb` and `0.72mg ` of `Sr^(87)`. Estimate the age of mineral pollucite stating any assumption made.

Answer

`5xx10^(8)years`

Explanation

`._(37)Rb^(87) rarr` `._(38)Sr^(87)+``_(-1)e^(0)`
Is is assumed that all the `Sr^(87)` originated by radioactive decay of `Rb^(87)`
`t_(1//2)` or `Rb=(0.693)/(K)=(0.693)/(1.1xx10^(-11)year^(-1))`
`=0.63xx10^(11)years`
Weight of `Rb^(87)` in the mineral pollucite
`=450mgxx(28)/(100)=126mg`
Weight of `Rb^(87)=126 mg ` which is present today is equal to `(a-x0`
Weight of `Sr^(87)=0.72mg` is the weight obtained after disintegration of `Rb^(87)=x`
`(` This has to be converted into weight of `Rb^(87))`
`87mg` of `Sr` is obtained from `87mg `of `Rb`.
`0.72mg` of `Sr` is obtained from `0.72 mg ` of `Rb`.
`:. (a-x)=126mg` ` x=0.72mg`
`a=126.72mg`
`t=(2.303)/(K)log``(a)/(a-x)`
`=(2.303)/(1.1xx10^(-11))log``(126.72)/(126)`
`=2.09xx10^(11)log 1.0057`
`=2.09xx10^(11)xx0.0024`
`=0.005xx10^(11)years`
`=5xx10^(8)years`