Final answer:
The variability of X-ray intensity across the primary beam is explained by interference when X-rays scatter off a crystal and the production of bremsstrahlung radiation and characteristic X-rays due to electron transitions in the target metal.
Step-by-step explanation:
The fact that X-ray intensity across the primary beam can vary as much as 45% describes the variability in intensity due to different processes that generate X-rays. When a beam of monochromatic X-rays strikes a crystal, the scattered X-rays undergo interference, leading to variations in intensity through constructive and destructive interference patterns. In the spectrum of X-ray radiation, apart from the continuous distribution of intensities due to bremsstrahlung, seen as a smooth curve, there are discrete spikes termed characteristic X-rays. These spikes correspond to specific energies at which electrons transition between energy levels in the metal atoms of the target material, and they provide a method for identifying the target metal. The classical electrodynamics description accounts for the smooth distribution of bremsstrahlung radiation, where accelerated charged particles emit a broad spectrum of radiation, while the characteristic peaks require a quantum mechanical explanation due to the quantization of atomic energy levels.