X-rays
Discussion
introduction
Electromagnetic waves
Reverse photoelectric effect
history
X-rays were discovered in 1895 by the German physicist Wilhelm Röntgen (also spelled Roentgen). He 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". Röntgen had a different idea.
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 appears to have always capitalized the x. I prefer to use lowercase, since the rays are purposely not named after any person, any place, or anything.
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.
1912: Walter Friedrich and Paul Knipping diffract x-rays in zinc blende
1912: Max von Laue suggests using lattice solids to diffract x-rays
1913: William Bragg and Lawrence Bragg work out the Bragg condition for strong x-ray reflection
1922: Arthur Compton studies x-ray photon scattering by electrons
Roentgen/Gas-Filled Tubes
The earliest x-ray tubes were filled with air at low pressure (or a partial vacuum, if you prefer)... cathode, anode, and anticathode.
 Source: bulbcollector.com a.k.a. kilocat |
 Source: photo by the author a.k.a. the author |
Coolidge/Vacuum Tubes
Most x-ray tubes in use today are "filled" with a vacuum. This "entirely new variety" of x-ray tube was invented in 1913 by the American electrical engineer William Coolidge (1873–1975). In that same year Coolidge developed the technique for making fine wire out of tungsten (a notoriously non-ductile metal). Nearly every incandescent light bulb made after 1913 contains a tungsten filament made using Coolidge's process. When he was done working on light bulbs, he turned his attention to x-ray tubes. Guess what? Nearly every x-ray tube made after 1913 contains a tungsten filament made using the process used in light bulbs.
In a typical vacuum x-ray tube, electrons accelerated from a heated cathode toward a metal anode by a large potential difference. Changing the filament temperature changes the electron current — a hotter cathode releases more electrons than a cold one. This determines the intensity or "brightness" of the x-ray beam. Since one electron will produce one x-ray photon when it strikes the anode, more electrons flying through the tube means more x-ray photons emitted from the tube. The voltage across the tube determines the kinetic energy of the electrons when they strike the anode, which in turn determines the penetrating power of the x-ray photons — more energy per electron means more energy per x-ray photon and thus greater ability to plow through matter.
The cathode is a coiled filament of wire (usually tungsten) heated to around 2000 °C (white hot). It emits electrons through thermionic emission. In a sense, the electrons "boil" off the metal surface, but it's a weird kind of boiling since the electrons that leave are always replaced by new ones. If I put a pot of water on the stove at home, set it boiling and then leave the kitchen for an hour or two, by the time I get back there's a good chance the pot will be empty (and maybe even sizzling red hot). This does not happen with electrons in a cathode. The ones that leave are always replaced with new ones. If they didn't we'd wind up with a collection of positively charged ions (and eventually bare nuclei) that would surely fly apart due to their mutual repulsion. An x-ray tube is a circuit element. Current goes in one end and out the other and round and round the circuit.
The anode is a comparatively massive copper heat sink whose target face is cut diagonally and coated with some other metal (usually platinum). More than 99% of the kinetic energy imparted to the electrons is converted to heat on the anode. The remaining 1% is emitted as braking radiation (i.e., useful x-rays). This heat must be transferred or the target would melt. Coolidge's solution was to rotate the target using a small motor. This ensured that the hot spot never stayed in one place long enough to cause any lasting damage to the anode. (Some x-ray tubes are cooled with water.) The target is cut on a diagonal so that the emitted x-rays fly off the surface at an angle different from the incident electrons. A 45° cut makes the x-rays exit perpendicular to the axis of the tube. All the photographs of x-ray tubes on this page have their targets aligned at this angle. (The photo of a dental x-ray tube shown below left is a bit distorted, so the geometry isn't apparent.)
 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
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characteristic vs. bremsstrahlung (braking) spectra.
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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 electric 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 electronvolts) 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
| λc = | 4π | E03 | |
| 3 | cBE2 |
which reduces to the following equation when the charged particles are electrons
| λc[nm] = | 1.86453 |
| B[T]E[GeV]2 |
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 nearly parallel rays (collimated) and is quite intense.
- Synchrotron radiation can be produced for hours, maybe even days if you were willing to pay the electric bils and had some reason to work around the clock. x-ray tubes can only operate for a few seconds or maybe minutes. Run them too long and they'll burn out just like a light bulb.
- Synchrotron radiation is "organized": the beam is highly polarized (most of the waves are oscillating in the same plane) and collimated (most of the waves are in the same direction). x-ray tubes produce "messy" radiation that is completely unpolarized and may be focused only with great difficulty. A synchrotron source is like an "x-ray laser", while an x-ray tube is like an "x-ray floodlight".
- Synchrotron radiation can be "shared". A large synchrotron might have upwards of 50 beam lines and run hundred if not thousands of experiments in one year. Synchrotron facilities are expensive to build, but pay for themselves in sheer volume of research.
- Wigglers or undulators (also known as insertion devices) produce synchrotron radiation that is considerably brighter than radiation from a bending magnet. The device causes electrons to follow a sinusoidal path instead of a curved one by establishing a series of magnetic fields that alternate in polarity and are perpendicular to the electrons' direction of travel. A wiggler enhances the brightness of the radiation produced by a given electron beam by a factor roughly equal to twice the number of full oscillations the beam undergoes. The deflections of the beam are smaller in an undulator than in a wiggler, and the radiation's brightness can, in theory, be increased by a factor about equal to the square of the number of oscillations, but only at discrete photon energies.
photon momentum
Max Planck discovered that phtons have energy.
E = hf
Albert Einstein discovered that energy and momentum are related.
E2 = p2c2 + m2c4
Photons are massless, so this equation reduces to…
E = pc
Combine Planck and Einstein (their equations, not the men themselves)…
hf = pc
Solve for momentum…
| p = | hf |
| c |
Recall that…
| λ = | c |
| f |
Thus…
| p = | h |
| λ |
If Planck and Einstein are correct, then photons have momentum too. What we need now is experimental evidence to support or refute this. (Don't worry. No one's going to refute this.)
compton effect
Arthur Compton (1892–1962) United States
| ∆λ = | 2h | sin2 | θ |
| mec | 2 |
technology
shadowgraphs
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computed axial tomography (CAT)
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x-ray scattering
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x-ray diffraction
Laue spots, Laue pattern. The German physicist Max von Laue (1879–1960) was the first to diffract X-rays on 12 April 1912.
Bragg's law. The father-son team of of British physicists William Bragg (1862–1942) and Lawrence Bragg (1890–1971) derived this equation in 1913.
nλ = 2d sin θ
where
| λ = | x-ray wavelength |
| n = | order |
| d = | separation between atomic planes |
| θ = | angle relative to the plane's surface |
DNA structure was determined from an x-ray diffraction image taken by Rosalind Franklin (1920–1958) England.
x-ray fluorescence
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