The Physics Boy

How X-Rays works?

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The photoelectric effect provides convincing evidence that photons. of light can transfer energy to electrons. ls the inverse process also possible? That is, can part or all of the kinetic energy of a moving electron be converted into a Photon? As it happens, the inverse photoelectric effect not only does occur but had been discovered (though not understood) before the work of Planck and Einstein.

In 1895 Willielm Roentgen found that a highly penetrating radiation of unknown nature is produced when fast electrons impinge on matter. These x-rays were soon found to travel in straight lines, to be unaffected by electric and magnetic fields, to pass readily through opaque materials, to cause phosphorescent substances. to glow, and to expose photographic plates. The faster the original electrons, the more penetrating the resulting x-rays, and the greater the number of electrons, the greater the intensity of the x-ray beam.

Not long after this discovery, it became clear that x-rays are em waves. Electromagnetic theory predicts that an accelerated electric charge will radiate em waves, and a rapidly moving electron suddenly brought to rest is certainly accelerated. Radiation produced under these circumstances is given the German name bremsstrahlung (”braking radiation”).

In 1912 a method was devised for measuring the wavelengths of x-rays. A diffraction experiment had been recognized as ideal, but as we recall from physical optics, the spacing between adjacent lines on a diffraction grating must be of the same order of magnitude as the wavelength of the light for satisfactory results, and gratings cannot be ruled with the minute spacing requited by x-rays. Max von Laue realized that the wavelengths suggested for x-rays were comparable to the spacing between adjacent atoms in crystals. He therefore proposed that crystal be used to diffract x-rays, with their regular lattices acting as a kind of three-dimensional grating. In experiments carried out the following year, wavelengths from 0.013 to 0.048 nm were found, 10-4 of those in visible light and hence having quanta 104 times as energetic.

Electromagnetic radiation with wavelengths from about 0.01 to about 10 nm falls into the category of x-rays. The boundaries of this category are not sharp the shorter wavelength end overlaps gamma rays and the longer, wavelength end overlaps ultraviolet light.

 

How X-Rays works
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A cathode, heated by a filament through whixh an electric current is passed, supplies electrons by thermonic emission. The high potential difference V maintained between the cathode and a metallic target accelerates the electrons towards the latter. The face of the target pass through the side of the tube. The tube is evacuated to permit the electrons to get to the target unimpeded.

As mentioned earlier, classical electromagnetic theory predicts bremsstrahlung when electrons are accelerated, which accounts in general for the x-rays produced by an x-ray tube However, the agreement between theory and experiment is not satisfactory in certain important respects. The image below show the x-ray spectra that result when tungsten and molybdenum targets are bombarded by electrons at several different accelerating potentials. The curve exhibit two features electromagnetic theory.

  1. In the case of molybdenum, intensity peaks occur indicate the enhanced production of x-rays at certain wavelengths. These occur at specific wavelengths for each target material and originate in rearrangements of the electron structures of the target atoms after having distributed by the bombarding electrons.
  2. The x-rays produced at a given accelerating potential V vary in wavelength, but none has a wavelength shorter than a certain value $\displaystyle {{\lambda }_{{\min }}}$. Increasing V decreases $\displaystyle {{\lambda }_{{\min }}}$. At a particular V, $\displaystyle {{\lambda }_{{\min }}}$ is the same for both the tungsten and molybdenum targets. Duane and Huntfound experimentally that $\displaystyle {{\lambda }_{{\min }}}$ is inversely proportional to V; their precise relationship is

$\displaystyle {{\lambda }_{{\min }}}=\frac{{1.24\times {{{10}}^{{-6}}}}}{V}V.m$

The second observation fits in with the quantum theory of radiation. Most of the electrons that strike the target undergo numerous glancing collisions, with their energy going simple into heat. This is why the targets in x-ray tubes are made from high melting-point metals such as tungsten, and means of colling the target is usually employed. A few electrons, though, lose most or all of their energy in single collision with target atoms. This is the energy that becomes x-rays.

X-rays production, then, except for the peaks, represents an inverse photoelectric effect. Instead of photon energy being transformed into electron KE, electron KE is being transformed into photon energy. A short wavelength means a high frequency, and a high frequency means a high photon energy hv.

Since work functions are only a few electron volts whereas the accelerating potentials in x-ray tubes are typically tens or hundreds of thousands of volts, we can ignore the work function and interpret the short wavelength limit as corresponding to the case where the entire kinetic energy KE=Ve of a bombarding electron is given up to a single photon of energy hvmax

Hence,

$ \displaystyle Ve=h{{v}_{{\max }}}=\frac{{hc}}{{{{\lambda }_{{\min }}}}}$

$ \displaystyle {{\lambda }_{{\min }}}=\frac{{hc}}{{Ve}}=\frac{{1.240\times {{{10}}^{{-6}}}}}{V}V\cdot m$

So, the above equation is appropriate to regard x-ray production as the inverse of the photoelectric effect

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