10.1.1 The Measurement of Concentration Using Natural Radioactive Isotopes

The quantity of an element present in the same sample can be determined if the rel­ative abundance of its isotopes is constant, and among these isotopes, there is at least one natural radioactive isotope with a long half-life. Such elements are potas­sium, rubidium, samarium, lutetium, rhenium, and uranium. In these concentration measurements, the activity of the radioactive isotopes is measured. When we know the relative abundance of the radioactive isotopes, the quantity of the element that is present can be calculated from Eq. (4.12), taking into account the relative abun­dance of the radioactive isotopes.

As an example, the data required for the quantitative measurement of lutetium is illustrated in Table 10.1. The 176Lu isotope, which is in the natural lutetium in 2.59%, is used for the measurements. As calculated from the data in Table 10.1, 10 4 mol of lutetium provide about 100 dpm of activity. This activity can be mea­sured easily by a 4n-counter (as described in Section 14.6). If other types of nuclear detectors are used, the measuring efficiency has to be included in the correction. Unfortunately, the half-lives of these very long-lived radioactive isotopes are fre­quently determined with a relatively high number of errors; thus, the quantitative measurements may have a high level of uncertainty.

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00010-X

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Table 10.1 The Data Required for the Quantitative Measurement of Lutetium Using

the 176Lu Isotope

Mass Number Relative Abundance (%) Half-life (min) Decay Constant (1/min)

175 94.71 Stable

176 2.59 2.02 X 10116 3.42 X 10“17