Chapter 2, Problem 93FP

Mass spectrometry is one of the most versatile and powerful tools chemical analysis because of its capacity to discriminate between atoms of different masses. When a sample containing a mixture of isotopes is introduced into a mass spectrometer, the ratio of the peaks observed reflects the ratio of the percent isotopic abundances. This ratio provides an internal standard from which the amount of a certain isotope present in a sample can be determined. This is accomplished by deliberately introducing a known quantity of a particular isotope into the sample to be analyzed. A comparison of the new isotope ratio to the first ratio allows the determination of the amount of the isotope present in the original sample.
An analysis was done on a rock sample to determine its rubidium content. The rubidium content of a portion of rock weighing 0.350 g was extracted, and to the extracted sample was added an additional 29.45 μg of ${}^{\text{27}}\text{Rb}$ . The mass spectrum of this speed sample showed a ²⁷Rb peak that was 1.12 times as high as the peak for ${}^{\text{27}}\text{Rb}$ . Assuming that the two isotopes react identically, what is the Rb content of the rock (expressed in parts per minion by mass)? The isotopic abundances and isotopic messes are shown in the table.