X-Rays

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Discussion

introduction

Electromagnetic waves

Reverse photoelectric effect

history


X-ray "shadowgraph" of a hand taken at the conclusion of Röntgen's first public lecture on x-rays. (Note the ring on the third finger.)

Wilhelm Conrad Röntgen also spelled Roentgen (1845-1923) Germany. Discovered x-rays in 1895. Received the first Nobel Prize in physics in 1901, "in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him." Wurzberg Physical-Medical Society, Chairman Albert von Kolliker, whose hand was used to to produce this image, proposed that this new form of radiation be called "Röntgen's Rays"

It is seen, therefore, that some agent is capable of penetrating black cardboard which is quite opaque to ultra-violet light, sunlight, or arc-light. It is therefore of interest to investigate how far other bodies can be penetrated by the same agent. It is readily shown that all bodies possess this same transparency, but in very varying degrees. For example, paper is very transparent; the fluorescent screen will light up when placed behind a book of a thousand pages; printer's ink offers no marked resistance …. A piece of sheet aluminium, 15 mm. thick, still allowed the X-rays (as I will call the rays, for the sake of brevity) to pass, but greatly reduced the fluorescence. Glass plates of similar thickness behave similarly; lead glass is, however, much more opaque than glass free from lead …. If the hand be held before the fluorescent screen, the shadow shows the bones darkly, with only faint outlines of the surrounding tissues. (Röntgen 1895)

Warning: don't try this at home. Don't try this anywhere!

The retina of the eye is quite insensitive to these rays: the eye placed close to the apparatus sees nothing. It is clear from the experiments that this is not due to want of permeability on the part of the structures of the eye. (Röntgen 1895)

production

Gas-filled tubes.

Early gas x-ray tubes.
Source: bulbcollector.com Source: photo by the author

Coolidge/vacuum tubes. Evacuated glass tube. Tungsten cathode at one end heated to around 2000 °C emits electrons through thermionic emission. In a sense, the electrons boil off of the metal surface. But it's a weird kind of "boiling" since the electrons can never evaporate away. They are always replaced by new ones. If they weren't we'd wind up with a huge positive charge on the metal surface.

Accelerated by a large potential difference (ranging from a few thousand to nearly a million volts depending on the application) toward a metal anode (a comparatively massive copper heat sink whose target face is cut diagonally and coated with some other metal). With a heated cathode in a high vacuum tube, the electron current may be controlled simply by varying the filament temperature. Then, by varying the voltage across the tube, the penetrating power of the x-rays (a function of the x-ray energy) may be varied. Thus, two important parameters may be controlled independently. More than 99% of the electrons' energy is converted to heat. This heat must be transferred or the target would melt. Water cooling is one method. In some tubes, the target face in mounted on a small motor.

Modern vacuum x-ray tubes.
Schematic diagram of "an entirely new variety of [x-ray] tube" from William Coolidge's 1913 patent application. Nearly all contemporary x-ray tubes are variations of the "Coolidge Tube". Source: US Patent & Trademark Office
A vacuum x-ray tube of the type used in dentistry. Source: bulbcollector.com

characteristic vs. bremsstrahlung (braking) spectra.

Hypothetical x-ray spectra produced by electrons with low energy (red), medium energy (green), and high energy (blue). As the energy of the electron beam increases, the maximum wavelength of the x-rays decreases but the location of the characteristic peaks does not.

brems (braking/deceleration) + strahlung (radiation)

In a cold pure metal (a), all electrons are below the Fermi energy level. Thermal energy allows electrons to form a space cloud in the vacuum (b), and application of an electric field allows the electrons to be collected on an anode; otherwise, an equilibrium is set up between the electrons inside and outside the metal. A tungsten wire is used in most X-ray tubes, electron microscopes and electron microprobes to take advantage of the high temperature for melting (3680 K) and evaporation. In a conventional X-ray tube, the wire is a coil approximately 1 cm by 1 mm, and the temperature is adjusted to minimize evaporation of W atoms which slowly contaminate the target. Unless an accelerating voltage is applied, there is no emitted current from a hot filament because of the formation of a space charge of electrons near the metal surface. The saturation current is measured by using the metal as a cathode of a vacuum tube and collecting the electrons on an anode which is sufficiently positive to dissipate the space charge. In a conventional X-ray tube, sufficient stability is obtained by regulating the filament voltage (for heating) and the accelerating voltage between cathode and anode.

There are two (THREE?) principal mechanisms by which x-rays are produced. The first mechanism involves the rapid deceleration of a high speed electron as it enters the electrical field of a nucleus. During this process the electron is deflected and emits a photon of x-radiation. This type of x-ray is often referred to as bremsstrahlung or "braking radiation". For a given source of electrons, a continuous spectrum of bremsstrahlung will be produced up to the maximum energy of the electrons.

X-rays are produced whenever fast moving electrons are decelerated, not just in x-ray tubes. Nearly all the naturally occurring x-ray sources are extraterrestrial. (No, that doesn't mean produced by alien creatures from outer space. It just means "beyond the earth".) X-rays are produced when the solar wind is trapped by the earth's magnetic field in the Van Allen Radiation Belts. Black holes are significant sources of x-rays in the universe. Matter falling into a black hole experiences an extreme acceleration caused by the intense field of the black hole. A single, isolated particle would fall in without releasing any radiation, but a stream of particles would as the particles would wind up crashing into each other on their way down the hole. Each inelastic collision experienced by a charged particle would result in the emission of a photon. Since these collisions are taking place at great speeds, the energies of the emitted photons in on the order of those found in the x-ray region of the electromagnetic spectrum. Inelastic collisions at even higher energies (greater than a million electron volts) would generate gamma rays.

The second mechanism by which x-rays are produced is through transitions of electrons between atomic orbits. Such transitions involve the movement of electrons from outer orbits to vacancies within inner orbits. In making such transitions, electrons emit photons of x-radiation with discrete energies given by the differences in energy states at the beginning and the end of the transition. Because such x-rays are distinctive for the particular element and transition, they are called characteristic x-rays.

The third mechanism is through synchrotron emission.

Initially predicted in 1944 by Ivanenko and Pomeranschuk in Russia, it was, three years later, accidentally observed in a closed ring accelerator of the type of a synchrotron. It was long viewed as a "waste product", because synchrotron radiation is produced in the accelerators as a magnetic bremsstrahlung and undesirably limits the required final energy of the accelerators. Only several years later, in 1956, was synchrotron radiation specifically used in scientific investigations by Tomboulian and Hartmann.

Synchrotron radiation is emitted by charged particles traveling on a curved path (as would happen while moving through a magnetic field). Since the source of all electromagnetic radiation is the acceleration of charge, synchrotron radiation is an example electromagnetic radiation produced by centripetal acceleration (as opposed to bremsstrahlung, which is produced by tangential acceleration). The wavelength of this radiation is a function of the energy of the charged particles and the strength of the magnetic field bending the charged particles. The spectrum of the radiation is continuous and is characterized by its critical wavelength, which divides the spectrum into two parts with equal power (half the power radiated above the critical wavelength and half below).

The critical wavelength can be found using the equation below

which reduces to the following equation when the charged particles are electrons

Synchrotron radiation sources: rings, undulators, wigglers, National Synchrotron Light Source doesn't produce light as its primary form of electromagnetic radiation. Most research done at this facility uses the x-rays and vacuum ultraviolet produced by the electron beam.

In 1945, the synchrotron was proposed as the latest accelerator for high-energy physics, designed to push particles, in this case electrons, to higher energies than could a cyclotron, the particle accelerator of the day. An accelerator takes stationary charged particles, such as electrons, and drives them to velocities near the speed of light. In being forced by magnets to travel around a circular storage ring, charged particles tangentially emit electromagnetic radiation and, consequently, lose energy. This energy is emitted in the form of light and is known as synchrotron radiation.

Synchrotron radiation is a nuisance in a particle accelerator as it sucks energy out of the particles being accelerated, but it makes an ideal source of high energy electromagnetic radiation. The beam produced is composed of very nearly parallel rays (collimated) and is quite intense.

The NSLS operates two electron storage rings: The VUV (vacuum ultraviolet) Ring operates at an electron energy of 800 MeV designed for optimum radiation at energies between 10 eV and 1 keV. The X-Ray Ring operates at 2.5 GeV to optimize radiation between 1 keV and 20 keV.

technology

shadowgraphs

computed axial tomography (CAT)

x-ray scattering

x-ray diffraction

x-ray fluorescence

Summary

Problems

practice

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numerical

  1. problems

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