22.08.2015   Nuclear and Radiochemistry

The Derivate Isotope Dilution Method

If the radioactive species of the substance to be analyzed is not available, the iso­tope dilution method cannot be applied directly. In this case, the substance to be analyzed is reacted with a radioactive reagent. This radioactive product can be then subjected to the reverse isotope dilution method (described in Section 10.1.6.2). The method, therefore, combines the preparation of a radioactive compound and the reverse isotope dilution method. The steps following the preparation of the radioactive compound are the same as for reverse isotope dilution. For example, the substance to be analyzed is A, the radioactive reagent is Bx, the excess of the reagent is Bm, and the derivate isotope dilution consists of the following steps:

A + Bx! ABx + Bm (chemical reaction) (10.5)

ABx 1 Bm + AB! (ABx 1 AB) 1 Bm (dilution) (10.6)

(ABx 1 AB) 1 Bm! (ABx 1 AB) (isolation) (10.7)

Similar to the other types of isotope dilution, the specific activities have to be determined before and after dilution, and the quantity of AB has to be known.

10.1.6.1 The Double Isotope Dilution Method

Double isotope dilution gives an opportunity to determine the quantity of a radioac-
tive substance (m0) if it is present in such small quantities that the specific activity

before the dilution (a0) cannot be determined. In this case, two aliquot samples are taken from the substance to be analyzed, and they are diluted with inactive isotopes in different quantities (m1 and m2, т1ф m2). After homogenization, the pure sub­stances of the two diluted samples are isolated and the specific activities (a1, a2) are measured. For the two dilutions, the following equation applies:

a0m0 = a(m0 + m) (10.8)

and

a0m0 = a2(m0 + m2) (10.9)

From Eqs. (10.8) and (10.9), we obtain:

aa2(m2 — m)

a0 =

(10.10)

a2m2 — am

am — a2m2

(10.11)

m0

a2 — a1

Thus, m0 can be calculated from the quantities m1 and m2 as well as the specific activities after the dilutions, a1 and a2.

The double isotope dilution method is applied in nuclear chemistry, organic, and biochemistry; however, it is the least accurate of the isotope dilution methods. This is because to determine the specific activities, a relatively large quantity of diluting substance has to be added. If m0 will become negligible compared to m1 and m2, the method cannot be applied.