The equivalent wavelength notion: Definition, properties, applications

Abstract The subject of a monochromatic radiation strictly equivalent to a given polychromatic spectral distribution is developed in accordance with usual analytical practice (e.g. by referring to relative intensities) assuming that (1) the polychromatic distribution can be any one, i.e. a continuous or discontinuous white spectrum, possibly including characteristic lines or not; (2) the fluorescent element is engaged in a homogeneous sample and is subject only to pure absorption effects (whether positive or negative) on the part of its neighbour elements. Important conclusions can then be derived. These are (a) the existence for each composition of one, and only one, equivalent wavelength λ e, the origin and mathematical determination of which are accurately described; (b) the fact that λ e systematically decreases with increasing fluorescent element concentration in binary compositions, whatever the associate element, whether it be a positive or negative absorber. This property then clearly extends to any given matrix; (c) the existence of a simple relation of equivalence between absorbers, enabling us to consider any absorber and then any absorbing matrix in terms of ‘equivalents’ if we so choose; (d) as a consequence of (b) and (c), a novel description of influence coefficients for the absorption case, accounting for their systematic variation with fluorescent element concentration and introducing a definite correlation between coefficients belonging to different absorbers; (e) further interesting properties such as the effect of the ‘geometry’, as well as the effect of dilution, on the situation of equivalent wavelengths and the values of influence coefficients. In so far as absorption effects are considered all the facts of X‐ray fluorescence as induced by polychromatic excitation are covered by the present theory.