characteristic radiation

Strike a bell and it rings at its own pitch; strike a different bell and you hear a different note. Metals do something similar with X-rays. When fast electrons hit a copper target, most of the X-rays come out as a smooth continuous blur, but riding on top of that blur are a few razor-sharp, intense spikes at wavelengths that belong to copper and copper alone. Those spikes are the characteristic radiation — the element's own X-ray fingerprint.

The mechanism is a two-step atomic reshuffle. An incoming electron knocks an electron clean out of an inner shell of a target atom — say the innermost K shell. That leaves a hole. An electron from a higher shell immediately drops down to fill it, and as it falls it releases the energy difference as a single X-ray photon of a precisely fixed energy (and therefore wavelength). A drop from the L shell to the K shell gives the K-alpha line; a drop from the M shell gives K-beta. For copper, K-alpha sits at about 1.5418 angstrom. Because the shell energies are set by the element's nuclear charge, the wavelengths are fixed by which metal you use — this regularity is Moseley's law.

This near-single-wavelength, intense line is exactly what diffraction needs, because Bragg's law connects one wavelength to one angle. In practice you keep the strong K-alpha and get rid of the weaker K-beta with a filter or monochromator. Common choices are copper (K-alpha near 1.54 angstrom), molybdenum (0.71 angstrom, more penetrating), and cobalt (1.79 angstrom, good for steels). One honest subtlety: what we call Cu K-alpha is really a close doublet, K-alpha-1 and K-alpha-2, with slightly different wavelengths; at high angles this splits each diffraction peak into two.