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X-Rays

Figure 1, Coolidge-type X-ray

X-rays are produced in  x-ray tubes such as the one shown in Figure 1.The high-voltage source is typically of the order of 103 to 106 volts. The electrons are emitted thermionically from the heated cathode and accelerated by the high voltage source toward a solid target called the anode which is made out of a metal of high atomic weight like tungsten, or metals like copper and molybdenum. Inside the tube, the electrons have a small probability of collision with air molecules since the gas pressure inside the gas is of the order of 0.01 Pa or 10-7 atm. After reaching the target, the electrons transfer energy in the form of electromagnetic radiation. These radiation is called X-rays. Since the incoming electrons beam  energy is of the order 35 keV, the electromagnetic radiation can be very energetic.  X-ray were originally produced by Wilhelm Röntgen in 1895.

Figure 2, Wavelength distribution of X-Ray production in a molybdenum target.

The X-ray production can be seeing as a continuous spectrum of radiation superimposed by two peaks of well defined wavelength. These two spectrum are called the Continuous X-Ray Spectrum and the Characteristic X-Ray Spectrum. Classical electromagnetic theory can not explain two elements of this experimental result,

  1. The picks of the characteristic x-ray spectrum; and,

  2. The existence of a minimal wavelength of the continuous x-ray spectrum.

Quantum atomic levels explain point one (see atom) while point two can be understood from the kinetic energy, , of the incoming electron corresponding to the potential energy of the electric potential between the cathode and the target, .  There is not more energy for the outcome x-ray. The quantization of this radiation implies that the x-ray photon has an energy

from where, .

 

 

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Continuous X-Ray Spectrum

The continuous spectrum correspond to the entire radiation spectrum ignoring the two well defined peaks. In this case the incoming electrons provide a limited amount of energy to the target atoms. This comparatively small amount of energy is carried by the emitted radiation in the form of X-Rays photons.

Figure 3

If K0 is the initial kinetic energy of the incident electron and DK is the change in energy of the electron, see Figure 3, the X-Ray photon has an energy given by |DK |= h f where h = 6.63 × 10-34 Js and f is the frequency of the emitted X-Ray photon.

The most energetic photon (greatest frequency) correspond to the case in which the total incident kinetic energy of the electron is transfer into the X-Ray photon,
 |
DK | = |-K0 |= h fmax from where the cutoff wavelength can be calculated

cutoff wavelength

 The cutoff wavelength is totally independent of the target material. However, the other characteristics of the spectrum depend on the target material.

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Characteristic X-Ray Spectrum

The two peaks of Figure 2, labeled Ka and Kb , are part of what is called the Characteristic X-Ray Spectrum. Similar peaks appear for greater wavelengths or smaller frequencies. The emission of characteristic X-Rays involves the following processes

Figure 4, Energy Levels Diagram for Molybdenum

  1. The energetic electrons collides with an atom of the target knocking out one of the most internal electrons of the atom (n small) creating a hole in the atomic structure of the atom.
  2. The hole is filled when an electron from a greater energy level from a middle shell of the atom (n mid value)  jumps down to the lower energy shell emitting a high energy photon (characteristic X-Ray).
  3. The electron from the middle shell is subsequently replaced by and electron from an upper energy shell which in the transition emits a low energy photon.