Module 8: From the Universe to the Atom

Thomson used a cathode ray tube - an evacuated glass tube with a cathode (negative electrode) and anode (positive electrode). When high voltage was applied, cathode rays traveled from cathode to anode, creating a visible beam that could be manipulated.

Key observations: The rays traveled in straight lines, were deflected by electric and magnetic fields (proving they carried charge), and produced the same deflection regardless of the cathode material (proving they were universal components of matter). The direction of deflection in electric fields showed the rays were negatively charged.

Thomson applied perpendicular electric and magnetic fields to the cathode ray beam. By adjusting the field strengths so the electric and magnetic forces exactly balanced, the beam traveled straight. This allowed him to calculate the velocity of the particles.

Force balance condition: When electric force equals magnetic force, the net force is zero and particles travel undeflected. Electric force is qE and magnetic force is qvB, so when qE = qvB, the velocity is v = E/B.

Determining q/m: With the magnetic field turned off, the electric field alone deflects the beam. The amount of deflection depends on the charge-to-mass ratio. By measuring the deflection and using the known velocity, Thomson calculated q/m ≈ 1.76 × 10¹¹ C/kg. This value was about 2000 times larger than that of the hydrogen ion, suggesting either the particle had much more charge or much less mass than any known ion.

Millikan sprayed tiny oil droplets into a chamber between two horizontal metal plates. The droplets became charged through friction during spraying. By applying a voltage across the plates, he created an upward electric force on negatively charged droplets. He adjusted the voltage until the electric force exactly balanced the gravitational force, suspending the droplet motionless in mid-air.

Force balance equation: When suspended, the upward electric force equals the downward gravitational force. This gives qE = mg, where q is the droplet's charge, E is the electric field strength, m is the droplet's mass, and g is gravitational acceleration. Rearranging: q = mg/E.

Determining droplet mass: By turning off the electric field and measuring the terminal velocity of the falling droplet, Millikan could calculate its radius using Stokes' Law (which relates terminal velocity to radius for viscous drag). From the radius and density of oil, he calculated the mass.

Millikan repeated the experiment with hundreds of droplets. Each droplet had a different charge, but a crucial pattern emerged: all measured charges were integer multiples of a fundamental value, approximately 1.602 × 10⁻¹⁹ C.

The charge on any droplet could be written as q = ne, where n is an integer (1, 2, 3, ...) and e = 1.602 × 10⁻¹⁹ C. This proved that electric charge is quantized - it comes in discrete packets, not continuous amounts. The smallest unit of charge, e, is the magnitude of charge on a single electron.

Determining electron mass: Combining Millikan's value of e with Thomson's measurement of q/m allowed calculation of the electron mass. Since q/m = 1.76 × 10¹¹ C/kg and q = 1.602 × 10⁻¹⁹ C, dividing gives m = 9.11 × 10⁻³¹ kg. This confirmed electrons are about 1/2000 the mass of a hydrogen atom.

The experiment: Alpha particles (helium nuclei with charge +2e) from a radioactive source were directed at extremely thin gold foil (about 400 atoms thick). A fluorescent screen surrounding the foil detected scattered alpha particles by producing tiny flashes of light where particles struck.

Expected result (Thomson model): If atoms were like plum pudding with diffuse positive charge, alpha particles should pass through with minimal deflection. The weak electric field from spread-out positive charge would cause only small-angle scattering.

Actual observations: Most alpha particles passed straight through with little or no deflection, suggesting atoms are mostly empty space. However, approximately 1 in 8000 particles deflected at large angles (greater than 90°), and some even bounced directly backward (180° deflection). Rutherford famously said this was "as if you fired a 15-inch shell at tissue paper and it came back and hit you."

Rutherford concluded that the atom must have a tiny, dense, positively charged nucleus containing most of the atom's mass. The large-angle deflections could only occur if alpha particles encountered an extremely concentrated positive charge. The fact that most particles passed through undeflected meant the nucleus occupies only a tiny fraction of the atom's volume.

Key features of the nuclear model: The nucleus is approximately 10⁻¹⁵ m in diameter, while the atom is about 10⁻¹⁰ m in diameter. This means the nucleus is 100,000 times smaller than the atom. If the atom were the size of a football stadium, the nucleus would be the size of a marble at the center. The nucleus contains all the positive charge and nearly all the mass. Electrons orbit at relatively large distances, making the atom mostly empty space.

Why large deflections occur: When an alpha particle approaches the nucleus closely, the strong Coulomb repulsion between the positive alpha particle and positive nucleus creates a large force. This force is inversely proportional to the square of the distance, so it becomes enormous at small separations. Only a concentrated charge can produce field strengths sufficient to reverse the direction of a fast-moving alpha particle.

Using his postulates, Bohr derived the energy levels of hydrogen:

The negative sign indicates the electron is bound to the nucleus. Energy increases (becomes less negative) as n increases. At n = ∞, E = 0, corresponding to a free electron.

Balmer Series (visible light): Transitions ending at n = 2 produce visible light. The Balmer formula can be derived from Bohr's energy levels:

Where R = 1.097 × 10⁷ m⁻¹ is the Rydberg constant, n_f is the final level, and n_i is the initial level. For the Balmer series, n_f = 2 and n_i = 3, 4, 5, ... producing red (656 nm), blue-green (486 nm), and violet (434 nm) lines.

Despite its success with hydrogen, the Bohr model had significant limitations that revealed its incompleteness.

Multi-electron atoms: The model failed to predict the spectra of atoms with more than one electron. Even helium's spectrum couldn't be accurately calculated because electron-electron interactions weren't properly accounted for.

Fine structure and hyperfine lines: High-resolution spectroscopy revealed that spectral lines actually consist of multiple closely-spaced lines. The Bohr model predicted only single lines and couldn't explain this splitting.

Zeeman effect: When atoms are placed in a magnetic field, spectral lines split into multiple components. The Bohr model couldn't explain this phenomenon, which arises from the quantization of angular momentum direction (not just magnitude).

Intensity predictions: The model couldn't predict the relative intensities of different spectral lines, which depend on the probability of transitions - a concept requiring quantum mechanics to properly describe.

De Broglie proposed that all matter has an associated wavelength given by:

Where λ is the de Broglie wavelength, h is Planck's constant, p is momentum, m is mass, and v is velocity. This relationship mirrors the photon momentum formula p = h/λ, extending it to particles with mass.

Why we don't see wave behavior in everyday objects: For macroscopic objects, the de Broglie wavelength is incredibly tiny. A baseball (mass 0.15 kg) moving at 40 m/s has wavelength λ = h/mv = (6.63 × 10⁻³⁴)/(0.15 × 40) ≈ 10⁻³⁴ m, far too small to observe. Wave effects only become noticeable when wavelength is comparable to the size of obstacles or apertures.

Clinton Davisson and Lester Germer provided experimental confirmation of de Broglie's hypothesis by demonstrating electron diffraction through a nickel crystal.

The experiment: A beam of electrons with known kinetic energy was directed at a nickel crystal. The regular atomic spacing in the crystal acted as a diffraction grating for the electron waves. Electrons scattered at specific angles showed intensity maxima and minima - a diffraction pattern exactly like that produced by X-rays with the same wavelength.

Results: The measured diffraction angles matched predictions using de Broglie's wavelength formula. For 54 eV electrons, the calculated de Broglie wavelength was 0.167 nm, which agreed perfectly with the wavelength determined from the diffraction pattern using the known crystal spacing. This proved electrons exhibit wave properties.

De Broglie's matter waves provided physical insight into Bohr's angular momentum quantization condition. If electrons are waves, stable orbits correspond to standing waves around the nucleus.

Standing wave condition: For a standing wave to exist around a circular orbit, the circumference must contain an integer number of wavelengths. This gives the condition:

Substituting de Broglie's wavelength λ = h/mv:

This is exactly Bohr's angular momentum quantization condition! De Broglie's hypothesis provided a wave interpretation: only orbits that fit an integer number of wavelengths are stable. Other orbits produce destructive interference and cannot exist. This explained why Bohr had to assume quantization rather than deriving it from first principles.

The wave function ψ is a mathematical function that contains all information about the electron's quantum state. However, ψ itself has no direct physical meaning - it can even be complex-valued.

Probability interpretation (Born): The square of the wave function magnitude, |ψ|², gives the probability density - the probability of finding the electron per unit volume at a particular location. High |ψ|² means high probability; |ψ|² = 0 means zero probability.

Electron clouds: Rather than precise orbits, we visualize electrons as probability clouds. Regions where |ψ|² is large appear as dense clouds, while regions where |ψ|² is small appear faint or empty. The electron isn't spread out like a cloud; rather, the cloud represents where we're likely to find the electron when we measure its position.

Solutions to Schrödinger's equation for hydrogen yield discrete energy levels, like Bohr's model, but with much more detailed structure. Each state is characterized by four quantum numbers.

Principal quantum number (n): Determines energy and approximate size of orbital. n = 1, 2, 3, ... corresponds to shells K, L, M, ... Energy increases with n, matching Bohr's formula E_n = -13.6/n² eV for hydrogen.

Angular momentum quantum number (ℓ): Determines orbital shape. ℓ = 0, 1, 2, ... (n-1) corresponds to orbital types s, p, d, f. Different ℓ values give different probability distribution shapes: s orbitals are spherical, p orbitals are dumbbell-shaped, d orbitals are more complex.

Magnetic quantum number (m_ℓ): Determines orbital orientation in space. m_ℓ = -ℓ, ..., 0, ..., +ℓ. For example, the three p orbitals (ℓ = 1) have m_ℓ = -1, 0, +1, oriented along different axes.

Spin quantum number (m_s): Describes intrinsic angular momentum of the electron. m_s = +½ (spin-up) or -½ (spin-down). This was added to Schrödinger's theory to explain fine structure and the Pauli exclusion principle.

The Schrödinger model successfully addressed all the limitations of the Bohr model.

Multi-electron atoms: The model extends naturally to atoms with many electrons using the same principles. While exact solutions exist only for hydrogen, approximation methods yield accurate results for all atoms.

Fine structure: When relativistic effects and spin-orbit coupling are included, the model predicts the splitting of spectral lines observed at high resolution.

Zeeman effect: The magnetic quantum number m_ℓ explains how spectral lines split in magnetic fields. Different m_ℓ states have different energies in a magnetic field, producing multiple spectral lines.

Chemical bonding: Orbital shapes and overlap explain chemical bonds. The Bohr model couldn't explain why atoms form molecules with specific geometries, but quantum mechanical orbitals predict molecular structure and bonding accurately.

Chadwick built on earlier work by Irène Joliot-Curie and Frédéric Joliot, who had observed that when beryllium was bombarded with alpha particles, it emitted highly penetrating radiation that could eject protons from paraffin wax (which contains hydrogen).

Key observation: The radiation from beryllium was uncharged (not deflected by electric or magnetic fields) and highly penetrating (unlike alpha or beta particles). When this radiation struck paraffin wax, protons were ejected with considerable energy. The Joliots incorrectly thought this was gamma radiation, but Chadwick recognized the energy transfer was inconsistent with photon collisions.

Chadwick applied conservation of momentum and energy to determine the properties of the mysterious radiation. If the radiation consisted of photons (gamma rays), the energy transfer to protons would be far too small to explain the observations. However, if the radiation consisted of particles with mass similar to protons, the collision dynamics worked perfectly.

The momentum argument: In a collision between a massless photon and a massive proton, momentum conservation requires the photon to transfer very little energy (like a ping-pong ball bouncing off a bowling ball). But Chadwick observed that protons were ejected with high speeds, implying a head-on collision with a particle of comparable mass.

Determining neutron mass: By measuring the velocities of ejected protons and applying conservation of momentum and kinetic energy in elastic collisions, Chadwick calculated that the mysterious particle had mass approximately equal to the proton mass. This particle was electrically neutral (hence not deflected by fields) and was named the neutron.

The strong nuclear force is a fundamental force that binds protons and neutrons (collectively called nucleons) together in the nucleus. It has several distinctive properties that distinguish it from other forces.

Short range: The strong force is extremely strong at distances less than about 1-3 femtometers (fm), but drops to essentially zero beyond about 3 fm. This is much shorter than electromagnetic forces, which follow inverse-square laws extending to infinity. The short range explains why the strong force only affects neighboring nucleons within the nucleus.

Charge independence: The strong force between two protons, two neutrons, or a proton and neutron is approximately the same. It doesn't depend on electric charge, unlike the electromagnetic force which only acts on charged particles.

Overcoming electrostatic repulsion: Inside the nucleus, protons are extremely close together (separated by about 1-2 fm). At these distances, the electromagnetic repulsion between positive charges would be enormous, but the even stronger nuclear force overcomes this repulsion and binds the nucleus together.

The Segrè chart plots neutron number (N) on the y-axis against proton number (Z) on the x-axis. Stable nuclei cluster along a "zone of stability" that reveals important patterns about nuclear structure.

Light nuclei (Z less than 20): For light elements, stable nuclei have approximately equal numbers of protons and neutrons (N ≈ Z). The zone of stability follows the diagonal line N = Z. Examples include carbon-12 (6 protons, 6 neutrons), nitrogen-14 (7p, 7n), and oxygen-16 (8p, 8n).

Heavy nuclei (Z greater than 20): As nuclei get heavier, more neutrons than protons are needed for stability (N greater than Z). The zone of stability curves above the N = Z line. For example, lead-208 has 82 protons but 126 neutrons. The extra neutrons are needed because they provide additional strong force attraction without adding electromagnetic repulsion, helping to overcome the increasing proton-proton repulsion in larger nuclei.

Upper limit: Beyond bismuth-209 (Z = 83), no stable nuclei exist. All nuclei heavier than bismuth are radioactive because the electromagnetic repulsion becomes too strong for even extra neutrons to stabilize the nucleus.

Unstable nuclei decay to move toward the zone of stability. The type of decay depends on how the nucleus deviates from stability.

Alpha decay (too heavy): Very heavy nuclei (typically Z greater than 82) are above the zone of stability and have too many nucleons total. They emit alpha particles (helium-4 nuclei) to reduce both proton and neutron numbers. Example: uranium-238 → thorium-234 + alpha.

Beta-minus decay (too many neutrons): Nuclei above the zone of stability (high N/Z ratio) convert a neutron to a proton via beta-minus decay: n → p + e⁻ + antineutrino. This moves the nucleus down and right on the Segrè chart, closer to stability. Example: carbon-14 → nitrogen-14 + electron + antineutrino.

Beta-plus decay or electron capture (too many protons): Nuclei below the zone of stability (low N/Z ratio) convert a proton to a neutron. This can occur via beta-plus emission (p → n + e⁺ + neutrino) or electron capture (p + e⁻ → n + neutrino). This moves the nucleus up and left toward stability. Example: sodium-22 → neon-22 + positron + neutrino.

Alpha particles are helium-4 nuclei consisting of 2 protons and 2 neutrons. Alpha decay occurs in heavy nuclei (typically Z greater than 82) and reduces both the atomic number and mass number.

Properties: Alpha particles are relatively massive (4 atomic mass units) and carry charge +2e. They travel at about 5% the speed of light and have high ionizing power because their double positive charge strongly interacts with electrons in matter. However, their large mass and charge mean they lose energy quickly through ionization. Alpha particles have low penetration - stopped by paper, skin, or a few centimeters of air. Despite low penetration, alpha emitters are dangerous if ingested or inhaled because they deposit all their energy in a small volume of tissue.

Example: Radium-226 undergoes alpha decay: $^{226}_{88}Ra \rightarrow ^{222}_{86}Rn + ^4_2He$. The atomic number decreases by 2 and mass number decreases by 4.

Beta decay involves the emission of electrons or positrons when a neutron converts to a proton or vice versa. There are two types of beta decay.

Beta-minus (β⁻): A neutron converts to a proton, electron, and antineutrino: n → p + e⁻ + ν̄. The atomic number increases by 1 while mass number stays constant. Example: carbon-14 → nitrogen-14 + e⁻ + ν̄.

Beta-plus (β⁺): A proton converts to a neutron, positron, and neutrino: p → n + e⁺ + ν. The atomic number decreases by 1 while mass number stays constant. Example: fluorine-18 → oxygen-18 + e⁺ + ν.

Properties: Beta particles (electrons or positrons) have charge ±e and very small mass. They travel at speeds up to 99% the speed of light and have medium ionizing power and medium penetration. Beta particles are stopped by a few millimeters of aluminum or a few meters of air. Beta radiation is more penetrating than alpha but less ionizing.

The neutrino: Initially, beta decay appeared to violate conservation of energy and momentum because the emitted electrons had a range of energies rather than a single value. Wolfgang Pauli hypothesized an invisible, uncharged, nearly massless particle (the neutrino) that carries away the missing energy and momentum. This prediction was later confirmed experimentally.

Gamma radiation consists of high-energy photons emitted when a nucleus transitions from an excited state to a lower energy state. Gamma emission usually follows alpha or beta decay when the daughter nucleus is left in an excited state.

Properties: Gamma rays are electromagnetic radiation (photons) with no mass and no charge. They travel at the speed of light and have very low ionizing power but very high penetration. Gamma rays can penetrate several centimeters of lead or meters of concrete. Shielding requires dense materials like lead or thick concrete barriers.

Nuclear transitions: Gamma emission doesn't change the atomic number or mass number - only the energy state of the nucleus changes. The notation often includes an asterisk or 'm' (metastable) to indicate an excited state. Example: cobalt-60 undergoes beta decay to excited nickel-60, which then emits two gamma rays: $^{60}_{27}Co \rightarrow ^{60}_{28}Ni^* + e^- + \bar{\nu}$ followed by $^{60}_{28}Ni^* \rightarrow ^{60}_{28}Ni + 2\gamma$.

Radioactive decay is a random process - we cannot predict when a specific nucleus will decay. However, for large numbers of nuclei, the decay follows exponential laws characterized by the half-life.

Half-life (t₁/₂): The time required for half of a sample to decay. After one half-life, 50% remains. After two half-lives, 25% remains. After n half-lives, (1/2)ⁿ or (0.5)ⁿ of the original sample remains.

Where N₀ is initial number of nuclei, Nₜ is number remaining after time t, and n is the number of half-lives elapsed.

Exponential form: The decay can also be written as $N_t = N_0 e^{-\lambda t}$, where λ is the decay constant related to half-life by $\lambda = \ln(2)/t_{1/2} \approx 0.693/t_{1/2}$.

The mass defect (Δm) is the difference between the total mass of separated nucleons and the actual mass of the nucleus.

Where Z is the number of protons, N is the number of neutrons, m_p is proton mass, m_n is neutron mass, and m_nucleus is the actual nuclear mass. The mass defect is always positive - the bound nucleus is lighter than its separated components.

Atomic mass units: Nuclear masses are typically measured in atomic mass units (u), where 1 u = 1.66054 × 10⁻²⁷ kg. The energy equivalent is 1 u = 931.5 MeV/c². This makes calculations more convenient: instead of converting mass to kg and using E = mc², we can directly convert mass defect in u to energy in MeV by multiplying by 931.5 MeV/u.

The binding energy (BE) is the energy required to completely separate all nucleons in a nucleus. It equals the energy released when the nucleus formed from separated nucleons.

Or in practical units: $BE \text{ (MeV)} = \Delta m \text{ (u)} \times 931.5 \text{ MeV/u}$

Binding energy per nucleon: To compare nuclear stability across different elements, we calculate binding energy per nucleon (BE/A, where A is mass number). This indicates how tightly bound each nucleon is on average. Higher BE/A means more stable nucleus.

The binding energy curve: A graph of BE/A versus mass number shows that iron-56 has the highest binding energy per nucleon (approximately 8.8 MeV per nucleon), making it the most stable nucleus. Nuclei lighter than iron can release energy through fusion (combining to form heavier, more stable nuclei). Nuclei heavier than iron can release energy through fission (splitting into lighter, more stable nuclei).

Fission is the splitting of a heavy nucleus into two lighter nuclei (fission fragments) plus several neutrons. This releases energy because the fission fragments have higher binding energy per nucleon than the original heavy nucleus.

Induced fission (Uranium-235): When U-235 absorbs a slow neutron, it becomes unstable U-236 which splits into fission fragments. A typical reaction is:

Multiple fission pathways exist with different fragment combinations, but all release 2-3 neutrons and approximately 200 MeV of energy per fission event. This energy comes from the increase in binding energy per nucleon when moving from uranium (BE/A ≈ 7.6 MeV) to medium-mass nuclei (BE/A ≈ 8.5 MeV).

Chain reaction: The neutrons released in fission can induce fission in other U-235 nuclei, creating a self-sustaining chain reaction. In nuclear reactors, the reaction is controlled using neutron-absorbing control rods. In nuclear weapons, the reaction is uncontrolled, releasing energy explosively. A critical mass is required for a sustained chain reaction - too small and too many neutrons escape without causing further fissions.

Fusion is the combining of light nuclei to form a heavier nucleus. This releases energy because the product has higher binding energy per nucleon than the reactants.

Deuterium-tritium fusion: The most readily achievable fusion reaction (used in experimental reactors) combines deuterium and tritium:

The Coulomb barrier: For fusion to occur, nuclei must overcome electrostatic repulsion to get close enough for the strong force to bind them. This requires extremely high temperatures (tens of millions of Kelvin) to give nuclei enough kinetic energy. At these temperatures, matter exists as plasma - ionized gas where electrons are stripped from atoms.

Fusion in stars: Stars generate energy through fusion. The Sun fuses hydrogen to helium via the proton-proton chain at core temperatures around 15 million K. More massive stars use the CNO cycle. When stars exhaust their hydrogen, they can fuse helium into carbon and oxygen (triple-alpha process) at higher temperatures. The most massive stars continue fusing heavier elements up to iron, beyond which fusion requires energy input rather than releasing it.

Fusion on Earth: Achieving controlled fusion for power generation is extremely challenging. The plasma must be confined at extreme temperatures without touching container walls (magnetic confinement in tokamaks) or compressed to extreme densities (inertial confinement using lasers). Fusion has advantages over fission: abundant fuel (deuterium from seawater), no long-lived radioactive waste, and no possibility of runaway chain reactions. However, sustained energy-positive fusion remains a major engineering challenge.

Fermions are particles with half-integer spin (1/2, 3/2, etc.) that make up matter. They obey the Pauli exclusion principle - no two identical fermions can occupy the same quantum state.

Bosons are particles with integer spin (0, 1, 2, etc.) that mediate the fundamental forces. They can occupy the same quantum state, unlike fermions.

Photon (γ): Massless, chargeless particle that carries the electromagnetic force. Photons mediate interactions between charged particles. They travel at the speed of light and have unlimited range (though intensity decreases with distance).

Gluons (8 types): Massless particles that carry the strong nuclear force. Gluons bind quarks together in hadrons and bind protons and neutrons in nuclei. Unlike photons, gluons themselves carry color charge and can interact with each other, making the strong force unique and complex.

W and Z bosons: Massive particles (W± and Z⁰) that carry the weak nuclear force. The W bosons are charged and mediate processes like beta decay where particle types change (neutron → proton + electron + antineutrino involves a W⁻ boson). The Z boson is neutral. These bosons are very massive (about 80-90 times the proton mass), which explains why the weak force has very short range.

Higgs boson: Discovered in 2012 at CERN, the Higgs boson is associated with the Higgs field that permeates all space. Particles acquire mass through their interaction with the Higgs field - stronger interaction means greater mass. Photons and gluons don't interact with the Higgs field, which is why they're massless.

Linear accelerators accelerate particles in a straight line using oscillating electric fields. Particles pass through a series of cylindrical electrodes (drift tubes) with alternating polarity.

Operating principle: The electric field between drift tubes accelerates particles. Inside each drift tube, particles drift at constant velocity (hence the name) because the conducting tube shields them from electric fields. The AC frequency is synchronized so that when a particle emerges from one drift tube, the polarity has switched and the next gap accelerates it forward. Each gap adds energy eV, where e is particle charge and V is voltage across the gap.

Drift tube length: Since particles gain speed at each gap, drift tubes must get progressively longer to maintain synchronization with the constant AC frequency. The Stanford Linear Accelerator (SLAC) is 3 km long and accelerates electrons to 50 GeV.

Advantages and limitations: Linacs can accelerate particles to very high energies in a single pass and don't suffer from synchrotron radiation energy losses (significant for circular accelerators with light particles like electrons). However, they require enormous length for highest energies and particles only pass through once, limiting collision rates.

Fundamental physics: Particle accelerators discovered the W and Z bosons (confirming electroweak theory), the top quark, the Higgs boson, and numerous other particles. High-energy collisions create conditions similar to the early universe, allowing physicists to test theories about fundamental forces and matter.

Medical applications: Cyclotrons and linacs produce radioisotopes for medical imaging (PET scans use fluorine-18 from cyclotrons). Linear accelerators deliver precisely targeted radiation therapy for cancer treatment, depositing energy in tumors while minimizing damage to healthy tissue.

Materials science: Synchrotron light sources (synchrotrons optimized to produce intense X-rays from accelerating electrons) allow researchers to study material structures at atomic resolution, from protein crystallography to semiconductor development.