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 c

Question

The isotopic composition of rubidium is R b 85 : 73 % R and R b 87 : 28 % R b 87 R is weakly radioactive and decay by β c − − β emission with a decay constant of 1.1 × 10 − 11 1.1 per year. A sample of the mineral pollucite was found to contain 450 g R b 450 and 0.72 m g 0.72 of S r 87 S . Estimate the age of mineral pollucite stating any assumption made. Select the correct answer from above options

Answer 1

Correct Answer - 5 × 10 8 y e a r s 5 . 37 R b 87 → . . 38 S r 87 + . _ ( − 1 ) e 0 _ Is is assumed that all the S r 87 S originated by radioactive decay of R b 87 R t 1 / 2 t or R b = 0.693 K = 0.693 1.1 × 10 − 11 y e a r − 1 R = 0.63 × 10 11 y e a r s = Weight of R b 87 R in the mineral pollucite = 450 m g × 28 100 = 126 m g = Weight of R b 87 = 126 m g R which is present today is equal to ( a − x 0 ( Weight of S r 87 = 0.72 m g S is the weight obtained after disintegration of R b 87 = x R ( ( This has to be converted into weight of R b 87 ) R 87 m g 87 of S r S is obtained from 87 m g 87 of R b R . 0.72 m g 0.72 of S r S is obtained from 0.72 m g 0.72 of R b R . ∴ ( a − x ) = 126 m g ∴ x = 0.72 m g x a = 126.72 m g a t = 2.303 K log t a a − x a = 2.303 1.1 × 10 − 11 log = 126.72 126 126.72 = 2.09 × 10 11 log 1.0057 = = 2.09 × 10 11 × 0.0024 = = 0.005 × 10 11 y e a r s = = 5 × 10 8 y e a r s =