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However, we know that the maximum amount of energy Emax which an electron can lose is the entire kinetic energy with which it arrived at the surface of the x-ray anode, equal (in Joules) to e Va where e is the electronic charge and Va the accelerating voltage applied to the x-ray tube.Therefore, However, the separation between an electron and a nucleus will be different at each collision and for different electrons, so a continuous distribution of wavelengths is produced. Quantum principle predicts that an x-ray photon of energy If an incoming electron passes an atomic nucleus at a particular distance and decreases its kinetic energy by an amount E, Einstein's Must lose energy in the form of electromagnetic radiation, and this is the origin of the bremstrahlung x-rays ( braking radiation in German). The principles of electromagnetism tell us that any charged particle undergoing acceleration (centripetal or not) This attraction will result in an angular deflection of the path of the electron and a brief period during which the electron undergoesĬentripetal acceleration. During this time, they will pass close to the positively charged nuclei of several atoms and will be attracted towards each nucleus. To understand the origin of the continuum, consider that electrons accelerated within the x-ray tube will travel some distance within the target before being brought to rest. The origin of the characteristic x-rays will be discussed later. The film) superimposed on a smoothly varying background (the bremststrahlung continuum). The spectrum recorded from a typical x-ray tube is seen to consist of some sharp peaks ( characteristic peaks, or lines as seen on The spectrum appears somewhat as shown in Fig.2.22b. If the film blackening is converted to intensity (using a device called a microdensitometer) We can record the spectrum of the x-rays. If we now slowly rotate the crystal, x-rays of different wavelength will strike a photographic film at different positions (see Fig. In other words, we can produce a monochromatic beam of x-rays, the reflecting crystal acting as a monochromator. , Bragg reflection provides us with of selecting photons of a particular wavelength from an incident beam containing a mixture of wavelengths. Since the equation is satisfied (for a particular angle of reflection) only for a single value of l This equation is known as Bragg's law, after the English physicist W.L. , where d is the interplanar spacing, so the condition for so-called Bragg reflection of the x-rays is: From geometry of the right-angled triangles ABD and BCD, AB = CD = d sin q Where n is any integer) the phase at points C and D on the wavefront of the reflected rays will also be the same and the two rays will combine constructively at the detector (e.g. If this extra distance is an integral number of wavelengths (AB + BC) further than the x-rays reflected from plane A. The x-rays reflected from plane B must travel an extra distance On a wavefront which is perpendicular to the incident direction. įor a parallel incident beam, the phase is the same at points (A and D in Fig. However this reflection takes place only for a particular angle of incidence, such that x-ray beams reflected from successive planes of atoms have their electric and magnetic fields in phase. In fact, the x-rays can be "reflected" from the atomic planes, as if the latter behaved like a mirror Photon energy or wavelength) by the nuclei of the atoms. The x-rays penetrate through many layers of atoms but at each layer there is a small probability of the x-rays being scattered elastically (with no change in Since atoms in a crystal are spaced regularly by a few hundreds of pm (some tenths of a nanometer, 1 nm = 10^-9 m) a crystal can be used as a kind of 3-dimensional diffraction grating to separate x-rays of different wavelengths. Within a few years it became clear that x-rays are another form of electromagnetic radiation, with wavelengths typically some tens or hundreds of picometers (1 pm = 10^-12 m).
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Within months, the first medical radiographs were produced, showing bones (which absorb x-rays more strongly) as darker areas on the photographic emulsion. He accelerated electrons (produced in vacuum by thermionic emission from a heated filament) towards a positive metal target (the anode) by applying several thousands of volts, and found that a very penetrating form of radiation is produced at the anode X-rays were discovered in 1895 by Wilhelm Roentgen. Figure references are to the second edition of Modern Physics by Serway, Moses and Moyer (Saunders, 1989).