108 X Rays: Atomic Origins and Applications

Every chemical element has its own unique set of electron energy levels and therefore its own characteristic electromagnetic spectrum. X rays occupy the high-frequency, high-energy region of the electromagnetic spectrum and are produced when electrons in atoms undergo transitions involving their innermost energy levels. In this section, we examine how x rays are generated, why each element produces characteristic x-ray energies, and how these properties are applied in medicine and scientific research.

Earlier in this text, we introduced x rays as part of the electromagnetic spectrum and discussed how an x-ray tube generates them. An x-ray tube accelerates electrons emitted from a heated filament through a large potential difference. These high-speed electrons collide with a metal target, called the anode, where their kinetic energy is converted into x rays and heat.

Two distinct physical processes produce x rays within the anode:

• Bremsstrahlung (braking radiation), which is produced when fast-moving electrons are rapidly decelerated by the electric fields of atomic nuclei.
• Characteristic x rays, which are produced when collisions remove electrons from the atom's inner electron shells and higher-energy electrons fall into the resulting vacancies.

The combined output of these two processes produces the spectrum shown in Figure 108.1. The broad continuous distribution is due to bremsstrahlung radiation, while the sharp peaks correspond to characteristic x rays whose energies depend on the material used for the anode.

The spectrum shown in Figure 108.1 represents the combined results of millions of electrons striking the anode. Most collisions transfer only part of an electron's kinetic energy to an x-ray photon, producing the broad range of bremsstrahlung photon energies. Occasionally, however, a single collision converts nearly all of an electron's kinetic energy into one photon. This produces the highest possible x-ray energy.

Conservation of energy relates the accelerating voltage of the x-ray tube to the maximum possible photon energy:

Because x-ray energies are typically expressed in electron volts, this relationship is especially convenient. For example, an x-ray tube operating at an accelerating voltage of 100 kV can produce photons with energies up to 100 keV.

Not every electron collision simply slows the incoming electron. Some collisions transfer enough energy to remove an electron from one of the atom's inner shells or excite it to a higher energy level. These vacancies are unstable because atoms naturally seek their lowest-energy configuration.

When an electron from a higher energy level falls into an inner-shell vacancy, the atom releases the energy difference as electromagnetic radiation. If the transition involves an inner shell, the emitted photon is an characteristic x ray.

The most energetic characteristic x rays occur when vacancies exist in the lowest electron shells. For example:

• A [latex]K_{\alpha}[/latex] x ray is produced when an electron falls from the [latex]n=2[/latex] shell into a vacancy in the [latex]n=1[/latex] shell.
• A [latex]K_{\beta}[/latex] x ray is produced when an electron falls from the [latex]n=3[/latex] shell into a vacancy in the [latex]n=1[/latex] shell.
• An [latex]L_{\alpha}[/latex] x ray is produced when an electron transitions from the [latex]n=3[/latex] shell to fill a vacancy in the [latex]n=2[/latex] shell.

The historical shell labels K, L, M, and N correspond to the principal quantum numbers [latex]n=1,2,3,\text{ and }4[/latex], respectively.

Because every element has a unique arrangement of electron energy levels, each element emits characteristic x rays with a unique set of energies. These characteristic energies serve as a fingerprint for identifying elements. Scientists use this property in environmental analysis, materials science, archaeology, forensic investigations, and biomedical laboratories to detect even trace amounts of specific elements.

Medical and Other Diagnostic Uses of X-Rays

X rays have become indispensable tools in medicine and many other fields. Most people are familiar with their use in dental and medical imaging (see Figures 108.4 and 108.5), where they allow healthcare professionals to examine structures inside the body without surgery. X rays are also widely used outside of healthcare—for example, to inspect luggage at airports (Figure 108.5), detect cracks in aircraft components, and examine manufactured parts for hidden defects. Today, the term x ray refers both to the high-energy electromagnetic radiation itself and to the image produced using that radiation. The phrase "to be x-rayed" has become part of everyday language because of the widespread use of this technology.

The simplest x-ray images are known as projection or shadow images. Because x-ray photons have much higher energies than visible-light photons, they can penetrate materials that are opaque to visible light. As x rays pass through an object, some photons are absorbed while others pass through to reach the detector. The resulting pattern of transmitted photons forms an image of the object's internal structure.

The penetrating power of an x ray depends primarily on its photon energy. Higher-energy x rays can pass through thicker or denser materials than lower-energy x rays. Consequently, the operating voltage of an x-ray tube is selected according to the part of the body being examined. For example, an x-ray tube operating at approximately 50 kV may be sufficient for imaging the chest, whereas imaging a broken leg enclosed in a cast may require voltages near 100 kV.

The appearance of an x-ray image also depends on the density of the material being imaged. Dense materials absorb more x rays, allowing fewer photons to reach the detector and producing darker shadows in the resulting image. This large difference in absorption makes x rays particularly effective for detecting bone fractures. They are also useful for identifying physiological structures, such as certain tumors, whose density differs from that of surrounding tissues.

Because x rays are highly energetic photons, they are capable of ionizing atoms and molecules. Ionization can damage biological tissues by altering molecules within cells, including DNA. Modern imaging equipment is therefore carefully designed to minimize radiation exposure while still producing images of sufficient quality for diagnosis. Radiation dose and the biological effects of ionizing radiation are discussed in the following chapter.

As x-ray photon energy increases, the Compton effect becomes increasingly important in the attenuation of x rays. During Compton scattering, an incoming x-ray photon collides with a loosely bound outer-shell electron. The electron gains kinetic energy and is ejected from the atom, while the scattered x-ray photon continues in a different direction with reduced energy.

When Compton scattering dominates, the probability that an x ray will be attenuated depends primarily on the number of electrons present in the material. Consequently, attenuation depends mainly on the material's density and thickness rather than on its atomic number, Z. This is one reason why distinguishing among different soft tissues using ordinary x rays can be difficult.

Lower-energy x rays generally produce images with higher contrast because differences in attenuation between tissues are larger. However, these lower-energy photons are also absorbed more readily and therefore cannot penetrate thick body regions as effectively. Imaging specialists must therefore balance image contrast against penetration when selecting the operating voltage for an x-ray examination.

Breast cancer is one of the leading causes of cancer-related deaths among women worldwide, making early detection especially important. Mammography uses low-energy x rays to detect suspicious regions of increased density within breast tissue. Although a mammogram cannot by itself determine whether a mass is malignant, it can identify abnormalities that require additional testing.

Obtaining high-contrast mammograms can be challenging because the x-ray absorption of many types of soft tissue is very similar. This difficulty is greatest in younger women, who typically have denser breast tissue. In older women, increased fat content often provides greater contrast between healthy tissue and tumors, making abnormalities easier to detect. Magnetic resonance imaging (MRI) is frequently used alongside mammography to improve detection rates and reduce false-positive findings in selected patients.

A conventional radiograph provides only a two-dimensional projection of a three-dimensional object. Dense structures such as bones may overlap and obscure soft tissues or organs located behind them. Taking images from different directions provides additional information, but important anatomical details may still remain hidden.

To overcome these limitations, modern medicine uses computed tomography (CT), also known as computed axial tomography (CAT). Instead of producing a single projection image, a CT scanner collects x-ray data from many different directions around the patient.

During a CT examination, a narrow beam of x rays passes through a thin section, or slice, of the patient's body. On the opposite side of the patient, an array of detectors measures the intensity of the transmitted x rays. The x-ray tube and detector array are mechanically linked so that they rotate together around the patient, collecting measurements from many different angles.

Powerful computer algorithms analyze the relative attenuation of the x rays along each path through the body and reconstruct a detailed cross-sectional image of the slice. As the patient slowly moves through the scanner, additional slices are acquired. These slices can then be combined to generate detailed three-dimensional representations of organs, bones, blood vessels, and other anatomical structures. In many cases, computer processing can further enhance specific tissues to improve diagnostic accuracy.

The development of computed tomography revolutionized medical imaging. In recognition of this achievement, Godfrey Hounsfield (United Kingdom) and Allan Cormack (United States) were awarded the 1979 Nobel Prize in Physiology or Medicine for their pioneering work on CT technology.

X-Ray Diffraction and Crystallography

Because x rays have very high photon energies, they also have very short wavelengths. For example, the 54.4-keV [latex]K_{\alpha}[/latex] x ray calculated in Example 108.1 has a wavelength of

This wavelength is much smaller than the dimensions of everyday objects, so x rays generally behave like rays when imaging macroscopic structures such as teeth or bones, producing sharp shadow images. However, atomic diameters are typically on the order of 0.1 nm, which is comparable to x-ray wavelengths. This makes x rays ideally suited for probing the arrangement of atoms within matter.

When x rays encounter a crystal or another regularly ordered structure, they are scattered by the atoms. Because the scattered waves originate from many different atoms, they interfere with one another. In some directions the waves reinforce each other (constructive interference), while in others they cancel (destructive interference). This phenomenon, known as x-ray diffraction, produces characteristic diffraction patterns that contain detailed information about the structure of the material.

By analyzing these diffraction patterns, scientists can determine the positions of atoms within crystals and even reconstruct the three-dimensional shapes of complex biological molecules. This technique, called x-ray crystallography, has become one of the most powerful experimental methods in chemistry, biology, materials science, and medicine.

Perhaps the most famous application of x-ray diffraction was the determination of the double-helix structure of DNA. In 1953, James Watson, Francis Crick, and Maurice Wilkins used x-ray diffraction data obtained by Rosalind Franklin to identify the molecular structure of DNA, fundamentally changing our understanding of genetics and molecular biology. Watson, Crick, and Wilkins received the 1962 Nobel Prize in Physiology or Medicine for this discovery. Rosalind Franklin, whose diffraction images were essential to the work, was not included in the award, a decision that has remained the subject of considerable historical discussion.

X-ray crystallography continues to play an essential role in modern science. In addition to confirming the size and shape of atoms, it reveals how atoms are arranged within materials. Researchers use this information to study everything from biological proteins and viruses to advanced materials such as high-temperature superconductors, whose remarkable electrical properties depend critically on the arrangement of atoms within their crystal lattices.

Historically, x-ray diffraction provided convincing evidence that x rays are electromagnetic waves. Soon after Wilhelm Röntgen discovered x rays in 1895, scientists suspected they were a form of electromagnetic radiation, but their extremely short wavelength made this difficult to prove experimentally.

In 1912, the German physicist Max von Laue proposed directing x rays through crystals. Because the spacing between atoms in a crystal was already known to be extremely small—comparable to the expected wavelength of x rays—he reasoned that a crystal should act as a three-dimensional diffraction grating. If a diffraction pattern could be observed, it would demonstrate both the wave nature of x rays and provide a way to measure their wavelength.

The experiments confirmed his prediction and provided the first direct evidence that x rays are electromagnetic waves. For this pioneering work, von Laue received the 1914 Nobel Prize in Physics.

The following year, the Nobel Prize in Physics was awarded jointly to Sir William Henry Bragg and his son Sir William Lawrence Bragg for developing x-ray spectrometers and establishing the new field of x-ray crystallography. Their methods transformed diffraction from a scientific curiosity into one of the most important tools for determining atomic structure.

William Henry Bragg began his academic career in Australia after emigrating from England, where he developed expertise in both physics and chemistry while teaching at the University of Adelaide. His son, William Lawrence Bragg, later returned to the Cavendish Laboratory in England, where he made major contributions to x-ray and neutron crystallography. Lawrence Bragg also supported many of the researchers who later solved the structures of biologically important molecules, including the DNA studies of Watson, Crick, Wilkins, and Franklin, as well as Max Perutz's Nobel Prize-winning work on the structure of hemoglobin.

The history of x-ray crystallography illustrates one of the defining strengths of physics: the development of experimental techniques and instruments that enable breakthroughs across many scientific disciplines. Advances in physics often provide the tools that allow researchers in chemistry, biology, medicine, and engineering to answer questions that would otherwise remain inaccessible.

X rays have many additional applications beyond medical imaging and crystallography. In radiation oncology, carefully controlled high-energy x rays are used to destroy cancer cells by damaging their DNA and preventing cell division. In astronomy, x rays emitted by neutron stars, black holes, supernova remnants, and other energetic cosmic objects provide important information about some of the most extreme environments in the universe.

X rays have also played significant roles in national security and environmental monitoring. Because nuclear explosions generate intense bursts of x rays, specialized detection systems can monitor the atmosphere for evidence of clandestine nuclear weapons testing.

Another important analytical technique is x-ray fluorescence (XRF). When x rays excite atoms in a material, the atoms emit characteristic x rays as they return to lower energy states. Measuring these characteristic emissions allows scientists to determine the elemental composition of a sample without destroying it. XRF is widely used in medicine, environmental science, geology, archaeology, art conservation, forensic science, and industrial quality control.

Section Summary

• X rays are high-frequency, high-energy electromagnetic radiation produced either when fast-moving electrons are rapidly decelerated (bremsstrahlung) or when electrons transition into vacancies in the inner electron shells of atoms, producing characteristic x rays.
• Characteristic x-ray energies are unique to each element because they depend on the atom's electron energy levels. This property allows x rays to be used for elemental identification as well as for medical and scientific applications.
• X rays are widely used in medicine for diagnostic imaging, including conventional radiography, mammography, and computed tomography (CT). They are also used in industry, security screening, and materials inspection.
• Because x-ray wavelengths are comparable to atomic dimensions, x-ray diffraction and x-ray crystallography can determine the atomic and molecular structure of crystals, proteins, DNA, and many other materials.

Conceptual Questions

9. Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.
10. Why does the energy of characteristic x rays become increasingly greater for heavier atoms?
11. Observers at a safe distance from an atmospheric test of a nuclear bomb feel its heat but receive none of its copious x rays. Why is air opaque to x rays but transparent to infrared?
12. Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.
13. Crystal lattices can be examined with x rays but not UV. Why?
14. CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.

Problems & Exercises

25. (a) What is the shortest-wavelength x-ray radiation that can be generated in an x-ray tube with an applied voltage of 50.0 kV? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.
26. A color television tube also generates some x rays when its electron beam strikes the screen. What is the shortest wavelength of these x rays, if a 30.0-kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these x rays from exposing viewers.)
27. An x ray tube has an applied voltage of 100 kV. (a) What is the most energetic x-ray photon it can produce? Express your answer in electron volts and joules. (b) Find the wavelength of such an x ray.
28. The maximum characteristic x-ray photon energy comes from the capture of a free electron into a [latex]K[/latex] shell vacancy. What is this photon energy in keV for tungsten, assuming the free electron has no initial kinetic energy?
29. What are the approximate energies of the [latex]K_{\alpha}[/latex] and [latex]K_{\beta}[/latex] x rays for copper?