Continuous and Characteristic X-Rays

Two distinct components in one beam. Spectroscopic analysis of the X-rays leaving a Coolidge tube (Section 1.7) -- plotting the intensity of X-rays produced against their wavelength -- reveals that the beam is not of a single kind at all, but a superposition of two physically distinct components (Figure 1): a smooth, continuously varying background, and a small number of sharp, intense spikes superimposed on top of it. Each is produced by a completely different physical process happening inside the target.

Continuous X-rays (bremsstrahlung). As a fast electron penetrates the target, it repeatedly passes close to the strong positive electric field of a target atom's nucleus, and is deflected and abruptly DECELERATED by the Coulomb attraction it experiences -- a sudden negative acceleration. Just as an accelerating charge radiates energy classically (the same principle behind why a Rutherford-model electron should have radiated continuously, Section 1.3), a decelerating electron radiates a photon carrying away the kinetic energy it loses in that one encounter. Because an electron can lose ANY fraction of its kinetic energy in a given encounter -- from a tiny sliver, in a distant near-miss, up to virtually the whole of it, in one close encounter -- the photons produced span a continuous, unbroken RANGE of energies (and hence wavelengths); this component is accordingly called the continuous X-ray spectrum, or bremsstrahlung (German for "braking radiation", describing exactly what produces it).

The short-wavelength limit $\lambda_{\min}$. Although the continuous spectrum covers a whole range of wavelengths, it does NOT extend down to arbitrarily short wavelengths -- it has a sharp, well-defined lower cut-off, $\lambda_{\min}$ (Figure 1). This limit occurs for the special (rare) case in which an incident electron loses its ENTIRE kinetic energy $eV$ in a SINGLE encounter, converting all of it into ONE photon of the maximum possible energy:

Since this expression involves only the electron's charge $e$, Planck's constant $h$, the speed of light $c$, and the accelerating voltage $V$, $\lambda_{\min}$ is completely INDEPENDENT of the target material -- a purely quantum result (Numerical 7 evaluates it for a typical tube voltage), with no counterpart at all in classical electromagnetic theory, which predicts no such minimum wavelength should exist. …