Theories explaining the dependence of characteristic X-ray intensity on particle size in heterogeneous materials are reviewed. Several discrepancies between the theories and between theory and experiment have been discovered. A new theory is proposed based on a more rigorous physical model. It is shown to explain well-established phenomena at least as precisely as do previous formulae. Excellent agreement is also obtained with new observations of the variation of characteristic X-ray intensity with packing degree and, in samples consisting of only one type of particle, with both packing degree and particle size. The same basic theory also predicts the observed variation of X-ray Intensity backscattered from or transmitted through a sample. It is also shown that similar results are obtained with particles suspended In a homogeneous matrix, such as an aqueous slurry.