The Physics of X-Rays: How We Learned to See Through Skin, Bones, and Entire Galaxies

The Accidental Discovery That Changed Medicine Forever

On the evening of 8 November 1895, Wilhelm Conrad Röntgen was alone in his laboratory at the University of Würzburg, running experiments with a Crookes tube — a partially evacuated glass tube that produces cathode rays (streams of electrons, though Röntgen didn’t know that yet) when a high voltage is applied. He had covered the tube in black cardboard to block the visible fluorescence. The room was dark.

And then he noticed something that shouldn’t have been happening. A small cardboard screen coated in barium platinocyanide, sitting on a bench nearly two metres away, was glowing.

Cathode rays couldn’t travel through air that far. They certainly couldn’t pass through the black cardboard wrapping. Something else was coming from the tube — something invisible, something that could penetrate opaque materials, something nobody had ever detected before.

Röntgen spent the next six weeks essentially living in his laboratory, methodically investigating these unknown rays. He found they passed through paper, wood, cloth, thin sheets of aluminium, and — most dramatically — human flesh. But they were stopped by dense materials like lead and bone. When he placed his wife Anna Bertha’s hand between the tube and a photographic plate, the developed image showed her skeleton, her wedding ring floating around a ghostly finger.

He called them X-rays. The X, he said, was for the unknown.

Within months, the first medical X-ray images were being taken in hospitals across Europe and North America. Within a year, X-rays were being used on battlefields to locate bullets in wounded soldiers. It may be the fastest translation from fundamental discovery to clinical application in the history of science.

Röntgen received the first-ever Nobel Prize in Physics in 1901. He refused to patent the technology, believing it should benefit all of humanity. And it has.

How X-Rays Are Born: Bremsstrahlung and Characteristic Radiation

To understand X-rays, you need to understand how they’re made. And the physics is, at its core, about what happens when very fast electrons hit very heavy atoms.

In a modern X-ray tube (not so different in principle from Röntgen’s original setup), a tungsten filament is heated until it emits electrons by thermionic emission — the same physics that powered vacuum tubes for a century. These electrons are then accelerated across a vacuum gap by a high voltage, typically 40,000 to 150,000 volts. By the time they reach the other side, they’re moving at a significant fraction of the speed of light.

Then they hit the target — a slab of tungsten (chosen for its high atomic number, high melting point, and ability to survive the brutal thermal load). And two things happen.

Bremsstrahlung — German for “braking radiation” — is what you get when a fast electron passes close to a tungsten nucleus. The intense electric field of the nucleus deflects the electron, changing its trajectory. Any charged particle that accelerates (or decelerates, or changes direction) emits electromagnetic radiation. The closer the electron passes to the nucleus, the more violently it’s deflected, and the more energetic the emitted photon.

This produces a continuous spectrum of X-ray energies, from nearly zero up to a maximum equal to the full kinetic energy of the incoming electron. If you accelerate electrons through 100,000 volts, the most energetic X-ray photon you can produce has an energy of 100 keV. Most bremsstrahlung photons have energies well below this maximum — the spectrum peaks at about one-third of the maximum energy and falls off to both sides.

Characteristic radiation is more selective. When an incoming electron has enough energy, it can knock an inner-shell electron completely out of a tungsten atom. This leaves a vacancy in a deep electron shell — the K-shell or L-shell, close to the nucleus. An electron from a higher shell immediately drops down to fill the vacancy, and the energy difference is emitted as an X-ray photon.

Because electron shell energies are fixed for each element — they’re determined by quantum mechanics — the emitted photons have very specific, discrete energies. For tungsten, the most prominent characteristic lines are the Kα lines at about 59 keV and the Kβ lines at about 67 keV. These sharp peaks sit on top of the broad bremsstrahlung continuum, like mountain peaks rising from a rolling plain.

Here’s a fact that might surprise you: X-ray production is extraordinarily inefficient. Only about 1% of the electron’s kinetic energy is converted to X-rays. The other 99% becomes heat. This is why X-ray tubes need aggressive cooling — often a rotating anode that distributes the thermal load over a larger area, sometimes water cooling, sometimes both. A medical X-ray tube operating at 100 kV and 200 mA dumps about 20 kilowatts of heat into a metal target the size of a coin. It’s a small, angry furnace.

How X-Rays Interact With Matter

The reason X-rays can see through you — and the reason different tissues look different on an X-ray image — comes down to three ways X-ray photons interact with atoms.

Photoelectric absorption is the clean kill. An X-ray photon is completely absorbed by an atom, knocking out an inner-shell electron. The photon disappears entirely. The probability of this happening increases dramatically with the atomic number of the absorbing atom — it scales roughly as Z⁴. This is the key to X-ray contrast. Calcium in bone (Z = 20) absorbs X-rays far more effectively than the carbon (Z = 6), nitrogen (Z = 7), oxygen (Z = 8), and hydrogen (Z = 1) that make up soft tissue. Lead (Z = 82) absorbs even more, which is why lead aprons are used for shielding.

Compton scattering is a partial interaction. An X-ray photon collides with an outer-shell electron, transferring some of its energy to the electron and continuing onward in a different direction with reduced energy. This is the dominant interaction for medium-energy X-rays in soft tissue, and it’s the main source of scattered radiation — photons that end up going in the wrong direction, fogging the image and contributing to patient dose without contributing to diagnostic information.

Pair production only happens above 1.02 MeV, when an X-ray photon converts into an electron-positron pair in the electric field of a nucleus. This is important in radiation therapy and high-energy physics, but irrelevant for diagnostic imaging, where photon energies rarely exceed 150 keV.

The practical result of these interactions is beautifully simple. When an X-ray beam passes through a patient, bones absorb most of the photons (high-Z calcium, strong photoelectric effect), soft tissues absorb some, and air-filled spaces absorb almost none. The pattern of transmitted X-rays — bright where they got through, dark where they didn’t — is the X-ray image.

But here’s the subtlety that took decades to master: the contrast between different soft tissues is poor in conventional X-rays. Muscle, liver, brain, and tumour all have similar compositions and similar X-ray absorption. This limitation is what drove the development of contrast agents (barium and iodine compounds that boost X-ray absorption in specific organs), CT scanning, and ultimately MRI — which uses an entirely different physics to distinguish soft tissues.

The Image: From Film to Digital

Röntgen’s original X-ray images were captured on photographic plates — glass coated with silver halide emulsion, the same chemistry used for photography. When X-ray photons hit the silver halide crystals, they trigger a photochemical reaction that, after development, leaves a pattern of dark silver grains. More X-rays, more darkening.

This basic approach — X-ray film — dominated radiology for nearly a century. It’s cheap, provides excellent spatial resolution, and creates a permanent physical record. But it has significant limitations: narrow dynamic range (the range of X-ray intensities it can capture before saturating or underexposing), no possibility of post-processing, and the need for chemical development.

Modern digital detectors have largely replaced film. There are two main types. Indirect detectors use a scintillator (typically caesium iodide) to convert X-ray photons to visible light, which is then detected by a photodiode array. Direct detectors use a semiconductor (typically amorphous selenium) to convert X-ray photons directly to electrical charge. Both produce digital images that can be viewed instantly, adjusted for brightness and contrast, transmitted electronically, and stored indefinitely.

The shift to digital has transformed radiology in ways that go beyond convenience. Digital subtraction angiography can remove the background anatomy to show only blood vessels by subtracting a pre-contrast image from a post-contrast one. Dual-energy imaging acquires two images at different X-ray energies simultaneously, allowing the decomposition of tissues into material-specific images — separating bone from soft tissue, or iodine contrast from calcium. These techniques are impossible with film.

CT: The Mathematics of Seeing in Slices

A conventional X-ray image is a flat projection — everything between the source and the detector is superimposed. Your ribs overlap your lungs. Your spine overlaps your heart. A tumour behind a bone might be invisible.

In 1971, Godfrey Hounsfield built the first clinical computed tomography scanner, and the problem of superposition was solved. (Allan Cormack had independently worked out the mathematical foundations earlier; they shared the 1979 Nobel Prize.)

The principle is elegant. Rotate an X-ray source and detector around the patient, acquiring absorption data from many angles — typically several hundred projections around a full 360° rotation. Then use a mathematical algorithm to reconstruct the X-ray absorption at every point in a cross-sectional slice.

The mathematics is based on the Radon transform, proved by Johann Radon in 1917 (the same year Einstein described stimulated emission — it was a productive year). The Radon transform shows that if you know the line integrals of a function along all possible lines through a plane, you can reconstruct the function exactly. Each X-ray measurement is precisely such a line integral — it measures the total absorption along the beam path. Collect enough of these, and you can compute the absorption at every point.

Modern CT scanners have moved far beyond Hounsfield’s original design, which took hours to acquire a single slice. Current scanners use a continuously rotating gantry with a wide detector array that captures multiple slices simultaneously (up to 320 slices per rotation), completing a full chest scan in less than a second. The X-ray tube rotates around the patient at up to four revolutions per second while the table moves smoothly through the gantry, tracing a helical (spiral) path through the body.

The spatial resolution of modern CT is about 0.5 millimetres — good enough to see individual coronary arteries, tiny lung nodules, and hairline fractures. The contrast resolution — the ability to distinguish tissues with slightly different densities — is far superior to conventional X-rays, which is why CT can differentiate grey matter from white matter in the brain, identify subtle liver lesions, and stage cancers with remarkable precision.

The cost is radiation dose. A chest CT delivers roughly 7 mSv — equivalent to about 350 chest X-rays, or roughly three years of natural background radiation. This isn’t negligible, and it’s why CT scans are prescribed judiciously. But for trauma assessment, cancer diagnosis, and surgical planning, the information is often irreplaceable.

X-Ray Crystallography: Seeing Atoms

The most scientifically consequential application of X-rays isn’t medical imaging — it’s crystallography.

In 1912, Max von Laue realised that if X-ray wavelengths were comparable to the spacing between atoms in a crystal (both on the order of angstroms, or tenths of nanometres), then crystals should diffract X-rays the way optical gratings diffract visible light. He was right. The resulting diffraction pattern — spots of constructive interference at specific angles — encodes the three-dimensional arrangement of atoms in the crystal.

William Henry Bragg and his son William Lawrence Bragg (the youngest Nobel laureate ever, at age 25) developed the mathematical framework for interpreting these patterns. Bragg’s law — nλ = 2d sin θ — relates the wavelength of the X-rays (λ), the spacing between crystal planes (d), and the angle of diffraction (θ). From the positions and intensities of the diffraction spots, the positions of individual atoms can be determined.

This technique has produced some of the most important discoveries in the history of science:

The structure of DNA. Rosalind Franklin’s Photo 51 — an X-ray diffraction pattern of hydrated DNA fibres — provided the crucial data that Watson and Crick used to build their double helix model in 1953. The X-shaped pattern immediately revealed a helical structure, and the spacing of the diffraction spots gave the pitch and diameter of the helix. It’s no exaggeration to say that molecular biology was born from an X-ray photograph.

The structures of proteins. Starting with myoglobin (John Kendrew, 1958) and haemoglobin (Max Perutz, 1960), X-ray crystallography has determined the atomic structures of over 200,000 proteins. Every rational drug design programme in the pharmaceutical industry relies on knowing the three-dimensional shape of the target protein — and most of that structural knowledge comes from X-rays.

The structure of materials. The arrangements of atoms in metals, semiconductors, minerals, superconductors, and virtually every other crystalline material have been determined by X-ray diffraction. The entire field of solid-state physics — and by extension, the semiconductor industry — rests on structural knowledge obtained from X-ray crystallography.

I find it remarkable that the same radiation Röntgen used to photograph his wife’s bones turned out to be the key to understanding the molecular architecture of life itself. Same physics, different scale, world-changing consequences both times.

Synchrotrons: The X-Ray Cathedrals

If you want really intense, really tuneable, really brilliant X-rays, you need a synchrotron.

A synchrotron is a particle accelerator — typically a ring hundreds of metres in circumference — that keeps electrons circulating at nearly the speed of light. When these relativistic electrons are forced to curve by powerful magnets, they emit electromagnetic radiation tangent to their path. This is synchrotron radiation, and at the energies involved, most of it comes out as X-rays.

The brilliance (photons per second per unit area per unit solid angle per unit bandwidth) of synchrotron X-ray sources is roughly 10¹² times higher than a conventional X-ray tube. That’s a trillion times brighter. The beam is also highly collimated, tuneable in wavelength (by adjusting the electron energy or using insertion devices), and pulsed — with pulse durations as short as picoseconds.

There are about 50 synchrotron light sources operating worldwide, and they’re among the most productive scientific instruments ever built. Users study protein structures, image ancient fossils in three dimensions without cutting them open, map chemical composition at the nanometre scale, probe catalytic reactions in real time, and study materials under extreme pressures and temperatures.

The newest generation — fourth-generation synchrotrons like MAX IV in Sweden, Sirius in Brazil, and the upgraded ESRF in France — use a lattice design called the multi-bend achromat that reduces the electron beam size and produces X-ray beams with almost laser-like coherence. These sources enable techniques like coherent diffraction imaging and ptychography, which can image non-crystalline materials at near-atomic resolution — no crystal required.

And then there are X-ray free-electron lasers (XFELs), like the European XFEL in Hamburg and LCLS in California. These produce X-ray pulses so short (femtoseconds) and so intense that they can image individual molecules before the molecule is destroyed by the radiation. The technique, called serial femtosecond crystallography, fires the X-ray pulse at a stream of tiny crystals. Each crystal is imaged and then obliterated, but the diffraction pattern from that single pulse — captured in femtoseconds — contains the structural information. Merge thousands of these single-shot patterns, and you get a complete structure.

It’s the ultimate smash-and-grab: photograph the molecule, destroy the molecule, use the photograph. The physics makes it possible because the image is formed faster than the atoms can move — even faster than they can respond to the enormous radiation damage.

The Dose Question: How Dangerous Are X-Rays, Really?

X-rays are ionising radiation. Each photon carries enough energy to eject electrons from atoms, break chemical bonds, and damage DNA. This is not a theoretical concern — the early pioneers of radiology paid a terrible price. Clarence Dally, Thomas Edison’s assistant and one of America’s most enthusiastic X-ray experimenters, died of radiation-induced cancer in 1904, one of the first recognised victims. Early radiologists routinely developed radiation burns, cataracts, and cancers from chronic, unprotected exposure.

Modern radiology has learned from these tragedies. The principle of ALARA — As Low As Reasonably Achievable — governs every diagnostic X-ray examination. But what are the actual risks?

Radiation dose is measured in sieverts (Sv), which account for both the energy deposited and the biological effectiveness of different radiation types. A standard chest X-ray delivers about 0.02 millisieverts (mSv). A mammogram delivers about 0.4 mSv. A CT scan of the abdomen delivers about 8 mSv. The average annual background radiation dose from natural sources — cosmic rays, radon gas in buildings, radioactive potassium in food, terrestrial gamma rays — is about 2.4 mSv.

The cancer risk from low-dose radiation is estimated using the linear no-threshold (LNT) model, which assumes that cancer risk is proportional to dose with no safe threshold. Under this model, a 10 mSv CT scan increases your lifetime cancer risk by roughly 0.05% — from a baseline of about 25% to about 25.05%. This is a real increase, but it’s tiny compared to the baseline risk and usually far smaller than the medical benefit of the scan.

That said, the LNT model at low doses is controversial. Some radiobiologists argue that very low doses might actually be harmless — that cellular repair mechanisms can handle the occasional broken DNA strand. Others argue the opposite — that low-dose radiation triggers genomic instability that makes future mutations more likely. The evidence is genuinely unclear at doses below about 100 mSv, because the statistical signal disappears into the noise of naturally occurring cancer.

What’s not controversial: unnecessary radiation should be avoided. Repeat imaging, scans that don’t change clinical management, and CT when a lower-dose technique would suffice — these are real problems. Paediatric doses are particularly concerning because children are more radiosensitive and have more years of life ahead in which a radiation-induced cancer could develop.

The physics of radiation protection is straightforward: time, distance, and shielding. Minimise exposure time. Maximise distance from the source (dose falls off as the square of distance). Place dense material (lead, concrete) between the source and people. Every radiology department in the world operates on these three principles, derived directly from the inverse-square law and the exponential attenuation of X-rays in matter.

X-Rays From Space

Röntgen produced X-rays in a vacuum tube. But the universe produces them on a vastly grander scale.

X-ray astronomy — observing celestial X-ray sources — became possible only after we could place detectors above Earth’s atmosphere, which absorbs X-rays completely. (This is why the sky doesn’t X-ray you, despite being full of cosmic X-ray sources.) The first cosmic X-ray source, Scorpius X-1, was discovered in 1962 by a sounding rocket experiment. It turned out to be a neutron star in a binary system, accreting matter from a companion star.

The physics is spectacular. Gas falling onto a neutron star or spiralling into a black hole is compressed and heated to millions of degrees — temperatures where thermal emission peaks in the X-ray band. The accretion disc around a stellar-mass black hole can reach temperatures of 10 million kelvin, producing X-rays with energies of several keV. The gas falling onto the neutron star surface is heated even further — to 100 million kelvin in extreme cases.

Galaxy clusters — the largest gravitationally bound structures in the universe — are filled with hot gas at 10 to 100 million kelvin, visible only in X-rays. This intracluster medium contains more mass than all the galaxies in the cluster combined. Without X-ray telescopes, we’d be missing most of the normal matter in the largest structures in the cosmos.

X-ray telescopes like Chandra (launched 1999) and XMM-Newton (launched 1999) have been producing astonishing science for over 25 years. But X-ray telescopes face a unique engineering challenge: X-rays pass through conventional lenses and mirrors (they’d just be absorbed or transmitted, not focused). Instead, X-ray telescopes use grazing-incidence mirrors — nested cylindrical shells where X-rays reflect at very shallow angles, like stones skipping off water. Chandra’s mirrors are so smooth that if they were scaled up to the size of Earth, the tallest bump would be about two metres high. That level of precision is why Chandra can resolve X-ray sources separated by less than an arc-second — comparable to reading a newspaper from half a kilometre away.

What X-Rays Teach Us

There’s a pattern in physics that I keep coming back to. Someone discovers a new way to see, and the world gets larger.

Before X-rays, the inside of a living body was invisible unless you cut it open. After X-rays, you could see bones, swallowed coins, bullet fragments, and tumours without a single incision. Medicine was transformed not by a new drug or a new surgical technique but by a new way of looking.

Before X-ray crystallography, the arrangement of atoms in matter was a theoretical abstraction — we knew atoms existed, but their precise positions in crystals, proteins, and DNA were unknown. After crystallography, we could see the double helix, the active site of an enzyme, the lattice of a semiconductor. An entire molecular world came into focus.

Before X-ray astronomy, the universe looked calm and steady — stars shining, galaxies spinning. X-ray eyes revealed a violent cosmos: matter being crushed onto neutron stars, gas at millions of degrees filling galaxy clusters, black holes devouring companion stars. The universe in X-rays looks nothing like the universe in visible light.

Each time, the physics was the same. Electromagnetic radiation at wavelengths too short for eyes to see, interacting with matter in ways governed by quantum mechanics and electrodynamics. But each application — medical, structural, astronomical — opened a door that couldn’t have been opened any other way.

Röntgen didn’t know what his rays were. He didn’t know they were electromagnetic waves. He didn’t know they would save millions of lives, reveal the structure of DNA, or show us black holes eating stars. He just noticed something glowing in a dark room when it shouldn’t have been.

And he had the sense to spend six weeks figuring out why.

That’s how physics works, more often than people realise. Not grand theories first and applications second, but a strange observation, a stubbornly curious person, and the discipline to follow the strangeness wherever it leads. The theory catches up eventually. The applications follow. But it starts with someone noticing a glow that shouldn’t be there and choosing not to ignore it.