view of isotope dilution but it illustrates the method's salient features. A more complex situation arises when the distinction between marked and unmarked fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of marked fish from previous field experiments; and vice versa, where the amount of marked fish added contains a small number of unmarked fish. In a laboratory setting, an unknown (the "lake") may contain a quantity of a compound that is naturally present in major ("blue") and minor ("yellow") isotopic forms. A standard that is enriched in the minor isotopic form may then be added to the unknown, which can be subsequently analyzed. Keeping to the fish analogy, the following expression can be employed: where, as indicated above, nA and nB represent the number of fish in the lake and the number of fish added to the lake, respectively; RA is the ratio of the native-to-marked fish in the lake prior to the addition of marked fish; RB is the ratio of the native-to-marked fish in the amount of marked fish added to the lake; finally, RAB is the ratio of the native-to-marked fish captured during the second visit. Applications Isotope dilution is almost exclusively employed with mass spectrometry in applications where high-accuracy is demanded. For example, all National Metrology Institutes rely significantly on isotope dilution when producing certified reference materials. In addition to high-precision analysis, isotope dilution is applied when low recovery of the analyte is encountered. In addition to the use of stable isotopes, radioactive isotopes can be employed in isotope dilution which is often encountered in biomedical applications, for example, in estimating the volume of blood. Single dilution method Consider a natural analyte rich in isotope iA (denoted as A), and the same analyte, enriched in isotope jA (denoted as B). Then, the obtained mixture is analyzed for the isotopic composition of the analyte, RAB = n(iA)AB/n(jA)AB. If the amount of the isotopically enriched substance (nB) is known, the amount of substance in the sample (nA) can be obtained: Here, RA is the isotope amount ratio of the natural analyte, RA = n(iA)A/n(jA)A, RB is the isotope amount ratio of the isotopically enriched analyte, RB = n(iA)B/n(jA)B, RAB is the isotope amount ratio of the resulting mixture, x(jA)A is the isotopic abundance of the minor isotope in the natural analyte, and x(jA)B is the isotopic abundance of the