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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. |
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Answer» Correct Answer - `5xx10^(8)years` `._(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` |
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