5.1 Atomic Structure & Electromagnetic Radiation

The Structure of the Atom

The atom is the smallest unit of an element that keeps that element's chemical identity. It has a dense central nucleus made of positively charged protons and neutral neutrons, orbited by negatively charged electrons arranged in discrete energy shells. The number of protons is the atomic number (Z), which defines the element (hydrogen Z=1, tungsten Z=74). The total of protons plus neutrons is the mass number (A). In a neutral atom, electrons equal protons, so there is no net charge. Atomic structure is the foundation for everything in x-ray physics: how x-rays are produced in the tube and how they later interact with tissue and contrast media.

Electron Shells and Binding Energy

Electrons occupy shells labeled outward from the nucleus: K, L, M, N, O, P, Q. Each shell holds a maximum of 2n^2 electrons, where n is the shell number. The octet rule limits the outermost (valence) shell to no more than 8 electrons, which governs chemical bonding.

Binding energy is the energy that holds an electron in its shell, expressed in kiloelectron volts (keV). It is greatest for the innermost K-shell electrons and for high-Z elements, because a larger nuclear charge pulls electrons more tightly. For tungsten (Z=74) - the standard target material of the diagnostic x-ray tube - the K-shell binding energy is about 69.5 keV and the L-shell about 12 keV. These specific numbers are testable, because both characteristic x-ray production (Section 5.2) and photoelectric absorption (Section 5.3) depend directly on binding energy.

Ionization Versus Excitation

When an incoming photon or particle transfers enough energy to eject an electron completely from its shell, the atom becomes a positively charged ion and the event is ionization. When the energy only lifts an electron to a higher shell without removing it, the event is excitation. X-rays and gamma rays are ionizing radiation precisely because their photon energy exceeds electron binding energies. Ionization is the biologically important interaction, because the resulting ion pairs can damage DNA (developed further in the radiobiology chapter).

Electromagnetic Radiation

X-rays belong to the electromagnetic (EM) spectrum, a continuum of energy that also includes (from low to high energy) radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays. Every form of EM radiation travels in a vacuum at the speed of light, c = 3 x 10^8 m/s, and shows wave-particle duality: it behaves as a wave with a wavelength and frequency, and simultaneously as a stream of particle-like energy packets called photons (or quanta).

The Wave and Particle Equations

The wave relationship is c = f x lambda, where f is frequency in hertz (cycles per second) and lambda is wavelength. Because c is constant, frequency and wavelength are inversely proportional - as wavelength gets shorter, frequency rises. The particle relationship is E = h x f, where h is Planck's constant. Combining the two shows that photon energy is directly proportional to frequency and inversely proportional to wavelength. This is why diagnostic x-rays, which have extremely short wavelengths (roughly 0.1 to 0.5 angstroms) and very high frequencies, carry enough energy to penetrate the body.

A useful shortcut for the exam is E(keV) = 12.4 / lambda(angstroms). For example, an x-ray photon with a wavelength of 0.25 angstroms has an energy of about 12.4 / 0.25 = 49.6 keV. Doubling the energy to about 99 keV requires halving the wavelength to 0.125 angstroms - a direct demonstration that shorter wavelength means higher energy.

Properties of X-rays

X-rays and gamma rays are physically identical; they differ only in origin. X-rays are produced outside the nucleus (in the electron cloud or by decelerating electrons in the tube target), while gamma rays originate from within the nucleus of a radioactive atom. Key properties tested by ARRT include: x-rays are highly penetrating, travel in straight lines at the speed of light, have no mass and no electrical charge, cannot be focused by a lens, are polyenergetic (a range of energies), produce secondary and scatter radiation, cause ionization and biologic change, produce fluorescence in certain materials, and affect image receptors and photographic film. Understanding that x-rays are uncharged and massless explains why they follow the inverse square law and why beam intensity - not just quality - depends on distance from the source.

Ionizing Versus Non-Ionizing Radiation

A critical dividing line on the EM spectrum separates non-ionizing radiation (radio, microwave, infrared, visible light, most ultraviolet) from ionizing radiation (x-rays, gamma rays, and the highest-energy ultraviolet). Only ionizing radiation carries enough per-photon energy to eject electrons and create ion pairs, which is why radiography is regulated for dose while a light bulb is not. A frequent exam trap is to assume a brighter (higher-quantity) beam is automatically more penetrating - it is not. Quantity (the number of photons) and quality (photon energy and penetrating power) are independent, exactly as they are for the x-ray beam described in Section 5.3.

Second Worked Example: Wavelength, Frequency, and Energy

Consider two photons with wavelengths of 0.10 and 0.40 angstroms. Using E(keV) = 12.4 / lambda, the first is 12.4 / 0.10 = 124 keV and the second is 12.4 / 0.40 = 31 keV. The shorter-wavelength photon carries four times the energy, confirming the inverse relationship between wavelength and energy and the direct relationship between frequency and energy. This is the same physics that lets a higher-kVp (higher-energy) beam penetrate a thick abdomen that a low-kVp beam cannot, and it is the conceptual bridge to how kVp controls beam quality in the sections that follow.