In the mathematical description it is assumed that no clustering occurs within the alloy. Then, for a binary alloy of the form , e.g. , the standard deviation of the composition is given by: 
where  is the number of atoms within the excitons' volume, i.e.  with  being the atoms per volume. 
In general, the band gap energy  of a semiconducting alloy depends on the composition, i.e. . The band gap energy can be considered to be the fluorescence energy. Therefore, the standard deviation in fluorescence is  
As the alloy broadening belongs to the group of inhomogeneous broadenings the line shape of the fluorescence intensity  is Gaussian: