Page 240 - Inorganic Mass Spectrometry - Fundamentals and Applications

226 Smith

We start with the following equation:
Ni Nis 3- Nit
R,=-=
Nk Nks + Nkt
This is simply the ratio of isotope i (sample) to isotope k (tracer or spike) in the
mixture of the two as measured by the mass spectrometer. Each isotope has a con-
tribution from each component of the mixture.
Because we want the concentration of the total element and not just that of
a single isotope, we modify the equation to include the total number of atoms in
the sample:

A few algebraic steps to solve for N, yield

N'(ait -
N, =
('~aks - ais)
emanging terns gives an expression in terms of isotope ratios:

Recall that Ns and Nt are the numbers of atoms in the mixture due to sample
and tracer, respectively. To convert them to weight requires use of the familiar Avo-
gadro relationship and involves multiply~ng both sides of the equation by 1 .O twice,
thereby introducing the atomic weights of sample and tracer (i.e., multiply each
side by AJA, and AIA,). Note that Avogadro's number appears on both sides of the
equation and cancels out. A, and A,, on the other hand, are not equal and do not
cancel. The resulting equation is one form of the isotope dilution equation.

In terms of concentration:

This formulation is only one of several that, although differing in notation
and in formulation of the collection of R terms, are algebraically identical. The
most co~on formulation seems to use Eq, (5.4) as the starting point for conver-
sion from atomic units to weight; see, for example, Faure [6] and Jarvis et al. [7].