X-rays
Radiation that sees through flesh and maps atoms.
Producing X-rays & Their Spectrum
Braking radiation plus fingerprint lines.
Slam fast electrons into a metal and the metal glows, not in visible light but in X-rays: photons a thousand times more energetic than light. Their spectrum has two parts: a smooth hump with a sharp edge, and spikes that fingerprint the metal.
A discovery by accident
In 1895 Wilhelm Röntgen was studying discharge tubes when he noticed that a fluorescent screen across the room glowed even though the tube was wrapped in black card. Something invisible was coming out where the cathode rays (fast electrons) hit the glass. He called the unknown radiation X-rays. They are electromagnetic waves, like light, with wavelengths roughly from 10 nm down to 0.001 nm.
The Coolidge tube
Modern X-ray tubes follow a design by W. D. Coolidge (1913):
- A highly evacuated glass tube, so electrons travel without hitting gas molecules.
- A filament (cathode) heated by a separate low-voltage supply gives off electrons (thermionic emission). The filament current controls how many electrons leave per second.
- A large voltage, typically tens of kilovolts, between filament and target accelerates them to high speed.
- The target is a metal with a high melting point and high atomic number (tungsten or molybdenum), set at an angle so X-rays leave through the side of the tube.
- Over 99 % of the electrons’ energy becomes heat, so the target sits on a thick copper block, often cooled by circulating oil or water.
Two kinds of X-rays
Measure the intensity of the X-rays at each wavelength and you get the graph below: a smooth continuous curve with sharp peaks sitting on top.
Continuous X-rays (braking radiation)
An electron arriving at the target has kinetic energy eV. Inside the metal it is slowed by the electric fields of the nuclei, and a decelerating charge radiates. An electron may lose its energy in many small steps, each giving a photon, so the photons have all energies up to a maximum. This radiation is also called bremsstrahlung, German for “braking radiation”.
The most energetic photon possible takes the whole kinetic energy of one electron in one go. That sets a sharp cutoff wavelength:
Characteristic X-rays
Sometimes an incoming electron knocks an electron right out of an inner shell of a target atom, say the K shell (n = 1). An electron from a higher shell then drops into the hole, and the energy released leaves as one X-ray photon. Because the shells’ energies are fixed by the element, these photons have definite wavelengths: the sharp peaks.
- Kα: an L electron (n = 2) fills a K vacancy.
- Kβ: an M electron (n = 3) fills a K vacancy; a bigger drop, so a shorter wavelength.
- Lα, Lβ…: electrons fill an L vacancy; much less energetic.
These lines only appear if the electrons have enough energy to create the vacancy in the first place. Below that voltage you see only the continuous spectrum. A heavy element such as tungsten needs about 70 kV to show its K lines.
Energy levels of the atom
It is neatest to talk about the energy of the whole atom. Take the normal neutral atom as zero. Removing a K electron takes energy EK, so an atom with a K vacancy has energy EK; with an L vacancy, a smaller EL; and so on. When an L electron fills the K hole, the vacancy moves to L and the photon carries off EK − EL.
Controlling a tube: intensity and quality
More filament current means more electrons per second, so more photons per second. The spectrum keeps its shape and cutoff, it is just taller.
A higher voltage gives every electron more energy, so λmin moves to shorter wavelengths and the whole hump shifts left. The X-rays penetrate further.
X-rays of short wavelength (high energy) penetrate a lot of material and are called hard X-rays; longer-wavelength ones are soft X-rays. Doctors pick the voltage for the job: soft rays for thin tissue, harder ones for thick parts of the body.
An X-ray tube runs at 40 kV. Find the highest frequency and the shortest wavelength of the X-rays it produces.
In a tube run at 30 kV, an electron loses 4 % of its kinetic energy in its first collision, and that energy comes out as a single photon. Find the photon’s wavelength.
A tube operates at 30 kV with a current of 0.8 mA through it. Find (a) how many electrons hit the target each second, (b) the energy delivered to the target per second, (c) the cutoff wavelength.
Copper’s Kα line has wavelength 154 pm. A copper atom with one K electron removed has energy 8.98 keV. Find the energy of a copper atom with one L electron removed.
Show that the frequency of the Kβ line equals the sum of the Kα and Lα frequencies. Then find the Kβ wavelength of an element whose Kα and Lα lines are at 71 pm and 540 pm.
- 1Coolidge tube: heated filament (current → number of electrons), high voltage (→ electron energy), cooled heavy-metal target.
- 2Continuous X-rays come from electrons braking in the target; they cut off sharply at λmin = hc/eV, independent of the target.
- 3Characteristic lines (Kα, Kβ, Lα…) come from filling inner vacancies; their wavelengths identify the element.
- 4Atom-energy picture: photon energy = E(vacancy before) − E(vacancy after); ν(Kβ) = ν(Kα) + ν(Lα).
- 5Higher voltage → harder, more penetrating X-rays; higher filament current → more intense X-rays.
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Moseley's Law
Atomic number is nuclear charge.
In 1913 a 26-year-old physicist measured the Kα lines of a long row of elements and found one simple straight line. It showed that an element’s identity is its nuclear charge, not its mass, and it put the periodic table on firm ground.
The pattern
Henry Moseley used crystals to measure the wavelengths of the characteristic X-rays from many different targets. Plotting the square root of the Kα frequency against the element’s position in the periodic table, the atomic number Z, gave a straight line:
Why the line is straight: Bohr’s model
For a single electron around a nucleus of charge Ze, Bohr’s model gives the photon frequency for a jump from n = 2 to n = 1 as ν = (3/4)RcZ². Now think of a heavy atom with one K electron missing. An L electron about to drop in sees the nucleus (+Ze) partly shielded by the one K electron still there, so it feels an effective charge of about (Z − 1)e. Replacing Z by Z − 1:
What it did for the periodic table
Before Moseley, elements were ordered by atomic weight, with a few awkward exceptions where chemistry demanded a swap. Moseley’s law showed that the real ordering number is Z, the charge of the nucleus:
- Cobalt and nickel: cobalt (atomic weight 58.93) is heavier than nickel (58.69), so ordering by weight put nickel first. Their X-ray lines put cobalt at Z = 27 and nickel at Z = 28, matching their chemistry.
- Gaps: missing points on the line revealed elements not yet discovered, at Z = 43, 61, 72 and 75. All of them were later found (technetium, promethium, hafnium, rhenium).
X-ray lines are now a standard way to identify which elements are present in a sample: X-ray fluorescence analysis.
The Kα wavelengths of copper (Z = 29) and molybdenum (Z = 42) are 154.1 pm and 70.9 pm. Find a and b in √ν = a(Z − b).
Using a = 4.97 × 10⁷ Hz½ and b = 1, estimate the Kα wavelength of iron (Z = 26).
- 1Moseley's law: √ν = a(Z − b) for a given characteristic line; b ≈ 1 for Kα.
- 2Bohr's model with the nucleus screened by one K electron gives ν = (3Rc/4)(Z − 1)², so a = √(3Rc/4).
- 3Elements are ordered by nuclear charge Z, not atomic weight (cobalt 27 before nickel 28).
- 4Gaps on the line predicted undiscovered elements; X-ray lines identify elements in a sample.
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Bragg's Law & Uses of X-rays
Crystals as gratings; X-rays at work.
X-ray wavelengths are about the size of the gaps between atoms, so a crystal acts as a natural diffraction grating for them. That lets us measure X-ray wavelengths and map where atoms sit. And their penetrating power has made them indispensable in hospitals, airports and factories.
Crystals as gratings
A diffraction grating works when its slits are spaced a few times the wavelength. For X-rays (around 0.1 nm) no ruled grating is fine enough, but in 1912 Max von Laue realised that the regular rows of atoms in a crystal, about 0.1–0.5 nm apart, would do the job. W. H. Bragg and his son W. L. Bragg then found a very simple way to think about it.
Bragg’s law
Picture the atoms arranged in parallel planes a distance d apart. An X-ray beam meets the planes at a glancing angle θ (measured from the plane, not from the normal). Each plane reflects a little of the beam, like a mirror. The ray reflected from the next plane down travels an extra distance of 2d sin θ. When that extra path is a whole number of wavelengths, all the reflected waves are in step and add to a strong beam:
Used one way round, a crystal of known spacing measures X-ray wavelengths (an X-ray spectrometer, which is how Moseley measured his lines). Used the other way, X-rays of known wavelength reveal the spacings and arrangement of atoms in a crystal: X-ray crystallography, which later revealed the structure of DNA and of countless proteins.
Copper Kα X-rays (λ = 0.154 nm) fall on a rock-salt crystal whose planes are 0.282 nm apart. At what glancing angles are strong reflections seen?
Properties of X-rays
- They are electromagnetic waves, so they travel at the speed of light and are not deflected by electric or magnetic fields (they carry no charge).
- They pass through many materials opaque to light; how easily depends on thickness, density and the atomic number of the material.
- They blacken photographic film and make some substances fluoresce.
- They ionize the gas they pass through and can eject photoelectrons from metals.
- They damage living cells.
Uses
| Field | How X-rays are used |
|---|---|
| Medicine: diagnosis | Bones absorb far more than flesh, so a radiograph shows fractures, swallowed objects, and diseases of the lungs and teeth. CT scanners combine many X-ray images into 3D maps. |
| Medicine: therapy | Carefully aimed hard X-rays destroy cancer cells and some skin growths. |
| Industry | Radiography finds hidden cracks and bubbles in welds, castings and engine parts without cutting them open. |
| Security | Airport and customs scanners see guns, explosives and smuggled goods inside luggage. |
| Science | Crystallography maps atoms; X-ray spectra identify elements; X-ray telescopes study hot gas around black holes. |
| Art and history | X-rays reveal earlier paintings under a canvas and check whether gems or artworks are genuine. |
- 1Crystal planes spaced d apart reflect X-rays strongly only when 2d sin θ = nλ (θ measured from the planes).
- 2Bragg's law measures X-ray wavelengths (with a known crystal) or crystal structure (with known X-rays).
- 3X-rays: electromagnetic, uncharged, penetrating, ionizing, fogging film, causing fluorescence.
- 4Uses: radiographs, CT, cancer therapy, flaw detection, security scanning, crystallography; all with care, since they harm living tissue.