The Physics
Opus in profectus


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Electromagnetic waves

Reverse photoelectric effect


X-ray shadowgraph
X‑ray shadowgraph of a hand wearing a ring taken at the conclusion of Röntgen's first public lecture on x‑rays (1896).

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.

Wilhelm Röntgen, 1895

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.

Wilhelm Röntgen, 1895

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.

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.)

characteristic vs. bremsstrahlung (braking) spectra.

brems (braking/deceleration) + strahlung (radiation)

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 third mechanism is through synchrotron emission.

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 =  E03
3 cBE2

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

λc[nm] =  1.86453

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.

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.

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

Recall that…

λ =  c


p = h

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

Cartoon representation of a photon scattering off an electron in an atom

∆λ =  2h  sin2  θ
mec 2




computed axial tomography (CAT)


x-ray scattering


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


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