X-rays were discovered by Röntgen in 1895. He was running a discharge tube covered in black paper when a fluorescent screen some distance away began to glow. The radiation passed through paper and wood, and since it passed through bone and flesh differently, it could make a photograph of the bones of a hand. Not knowing what it was, Röntgen called it X-rays.
In an X-ray tube, a heated cathode inside an evacuated tube gives off electrons, and a high voltage accelerates them toward the anode. With an accelerating voltage V, an electron reaching the anode has kinetic energy eV. At 30 kV, eV is 30 keV and the electron moves at about one third of the speed of light.
An electron entering the metal of the anode, the target, is deflected by the electric field each time it passes near a nucleus, and slows down until it stops. An accelerated charge gives off electromagnetic waves, so waves of very short wavelength come out here. These are X-rays. Only about 1% of the electrons' energy becomes X-rays and the rest becomes heat, so the target is made of a metal with a high melting point such as tungsten and is cooled while in use.
X-ray wavelengths are about 0.01 to 1 nm, a few thousandths of those of visible light. The lines of an ordinary diffraction grating are too far apart to measure them. In 1912, following an idea of Laue, it was shown that X-rays passing through a crystal produce a pattern of diffraction spots on a photographic plate. The regularly arranged atoms in a crystal can serve as a diffraction grating.
The next year, 1913, the Braggs, father and son, wrote the condition for X-rays reflected from the planes of atoms in a crystal to reinforce each other as 2d\sin\theta = n\lambda. Here d is the spacing of the planes, \theta the angle between the planes and the X-rays, and n an integer.
In a crystal of rock salt the planes are 0.282 nm apart, so measuring the angles of strong reflection gives the wavelength. An instrument that turns the crystal and measures the strength of the reflected X-rays at each angle is called an X-ray spectrometer. All the X-ray spectra in this article were measured this way.
Measuring the X-rays from a target wavelength by wavelength with an X-ray spectrometer gives a shape made of two parts: a smooth curve with some strength at every wavelength, and sharp lines where a few particular wavelengths are far stronger than the rest. The smooth part is called the continuous X-rays and the lines the characteristic X-rays.
The continuous X-rays are given off as electrons slow down in the target, and are also called bremsstrahlung. The shape of the smooth curve is set mainly by the accelerating voltage: raising the voltage raises the whole curve and moves the wavelength of greatest strength toward shorter wavelengths. Changing to a target of higher atomic number raises the curve roughly in proportion to the atomic number, but hardly changes its shape.
The characteristic X-rays appear at wavelengths fixed by the element of the target: 0.154 nm and 0.139 nm for copper, 0.071 nm and 0.063 nm for molybdenum. Changing the accelerating voltage does not move them; only changing the target does. The two parts arise in different ways, so the continuous X-rays are taken up first.
Toward shorter wavelengths, the strength of the continuous X-rays falls and reaches 0 at a certain wavelength. No X-rays shorter than that come out at all. This wavelength is called the shortest wavelength, written \lambda_{\mathrm{min}}.
\lambda_{\mathrm{min}} stays the same when the target is changed from tungsten to copper or molybdenum. It moves only when the accelerating voltage is changed, and doubling the voltage halves \lambda_{\mathrm{min}}. What sets the shortest wavelength is not the material of the target but the energy of the electrons that strike it.
Classical electromagnetism cannot account for this. The spread of wavelengths radiated by a decelerating charge depends on how it decelerates, and the more abruptly it slows, the more short-wavelength radiation it gives off. An electron passing very close to a nucleus can be deflected as abruptly as one likes, so the strength should fall off smoothly toward short wavelengths, with no reason to reach zero at any particular wavelength. The dashed curve in the figure shows this expectation.
If X-rays are taken to be photons, the shortest wavelength follows at once. An electron in the target slows down by giving off photons each time it passes near a nucleus. The energy of each photon equals the energy the electron lost at that moment, and since the electron usually loses its energy over many such events, each photon has less than eV.
A photon has the most energy when the electron loses all of its energy at once. Then eV = h\nu_{\mathrm{max}}, and rewriting with \nu = \dfrac{c}{\lambda} gives \lambda_{\mathrm{min}} = \dfrac{hc}{eV}. This is the Duane-Hunt law, confirmed in 1915 by Duane and Hunt, who measured \lambda_{\mathrm{min}} while changing the voltage.
Using hc = 1240 eV·nm, with \lambda_{\mathrm{min}} in nm and V in kV, \lambda_{\mathrm{min}} = \dfrac{1.24}{V}. At 30 kV this is 0.041 nm, and at 100 kV 0.0124 nm. Nothing about the target appears in the formula, so the value is the same for every metal.
Measuring the voltage and \lambda_{\mathrm{min}} gives h. Since e and c are known from other measurements, h = \dfrac{eV\lambda_{\mathrm{min}}}{c} can be computed, and the h found this way agreed with the values from blackbody radiation and from the photoelectric effect.
In the photoelectric effect, the energy h\nu of one photon became the kinetic energy of one electron. Here, the other way round, the kinetic energy eV of one electron becomes the energy of one photon. For this reason, the process that produces the shortest-wavelength X-rays is also called the inverse photoelectric effect.
Electrons in an atom can only be in states of definite energy; this is taken up in the articles in the category on energy levels of atoms. Here only one fact is used: there are shells of electrons, called the K, L and M shells from the inside out, and the electrons of the inner shells are held more strongly by the nucleus.
An electron entering the target sometimes knocks an electron out of the K shell of an atom. When the K shell has a vacancy, an electron from the L or M shell moves into it, and the difference in energy between the two states comes out as one photon. The line from an electron coming from the L shell is called K_\alpha, and the line from one coming from the M shell K_\beta.
The energies of the shells are fixed by the element, so the wavelengths of the lines are too, and changing the accelerating voltage does not move them. Knocking out a K-shell electron does, however, require an eV larger than its binding energy. For copper this is 8.98 keV, so below 8.98 kV no K lines appear. The K_\alpha line of copper has an energy of 8.05 keV and a wavelength of 0.154 nm.
In 1913 Moseley measured the frequency of the K_\alpha line for targets made of the elements from calcium to zinc (atomic numbers 20 to 30), and found that its square root is proportional to the atomic number Z minus 1. The energy of K_\alpha is close to 10.2 \times (Z - 1)^2 eV; for copper (Z = 29) this gives 8.0 keV, in agreement with the measured 8.05 keV.
10.2 eV is the energy given off when the electron of a hydrogen atom moves from the second state to the first. The K shell normally holds two electrons, and the one that remains after the vacancy forms screens e of the nuclear charge Ze. The electron that moves in is then attracted as if by a nucleus of charge (Z - 1)e, and its energy is (Z - 1)^2 times that for hydrogen.
Moseley's measurements made it clear that the order of the elements is set not by the mass of the atom but by the charge Z of the nucleus. By mass, cobalt (58.93) would come after nickel (58.69), but K_\alpha gives cobalt 27 and nickel 28. Numbers missing from a sequence in which Z should rise by one each time also showed that the elements 43, 61, 72 and 75 had not yet been found.