Chapter 25, Problem 74FP

Radioactive decay and mass spectrometry are often used to date rocks after they have cooled from a magma. $Rb$ has a half-life of $4.88\times {10}^{10}$ years and follows the radioactive decay
$Rb\to Sr+{\beta }^{-}$
A rock was dated by assaying the product of this decay. The mass spectrum of a homogenized sample of rock showed the $Sr/Sr$ ratio to be 2.25. Assume that the original $Sr/Sr$ ratio was 0.700 when the rock cooled Chemical analysis of the rock gave 15.5 ppm Sr and 265.4 ppm Rb. using the average atomic masses from a periodic table. The other isotope ratios were $Sr/Sr=0.119$ and $Sr/Sr=0.007$ The isotopic ratio for $Rb/Rb$ is 0.330. The isotopic masses are as follows:

Calculate the following:
the average atomic mass of Sr in the rock
a. the original concentration of Rb in the rock in ppm
b. the percentage of rubidium-87 decayed in the rock
c. the time since the rock cooled