30.4 X Rays: Atomic Origins and Applications

X-rays revolutionized medical imaging, allowing doctors to see inside the body without surgery. These electromagnetic waves are produced when electrons hit a metal target in an x-ray tube, creating both continuous and characteristic spectra.

X-rays interact with matter through the photoelectric effect and Compton scattering. In medical applications, they're used for radiography and CT scans. Safety is crucial, as x-rays can cause biological effects, so dose reduction techniques are essential.

X-Ray Production and Characteristics

Structure and function of x-ray tubes

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• X-ray tube components consist of a cathode, which is a heated filament that emits electrons, an anode, which is a metal target that electrons collide with to produce x-rays, and a vacuum tube that allows electrons to accelerate from the cathode to the anode
• Electron acceleration occurs when a high voltage is applied between the cathode and anode, causing electrons to accelerate from the cathode to the anode
• X-ray generation happens when electrons collide with the anode material, producing two types of x-rays: bremsstrahlung (braking radiation), which has a continuous spectrum, and characteristic x-rays, which have discrete energy peaks
• The x-ray spectrum consists of a continuous bremsstrahlung spectrum, where the minimum wavelength ($\lambda_{min}$) is determined by the maximum electron energy according to the equation $\lambda_{min} = \frac{hc}{eV}$, where $h$ is Planck's constant, $c$ is the speed of light, $e$ is the electron charge, and $V$ is the accelerating voltage, and characteristic x-ray peaks that are specific to the anode material and result from electron transitions between inner atomic shells (K, L, M)
• X-rays are part of the electromagnetic spectrum, with wavelengths between ultraviolet light and gamma rays

Characteristic energy of x-rays

• Characteristic x-ray energy is determined by electron transitions in the anode material, specifically electron transitions between inner atomic shells such as K, L, and M shells
• The energy of characteristic x-rays can be calculated using the equations $E = hf$, where $E$ is the x-ray energy, $h$ is Planck's constant, and $f$ is the frequency, or $E = \frac{hc}{\lambda}$, where $\lambda$ is the wavelength
• Characteristic x-ray notation includes the K-series, which involves transitions to the K-shell (n=1) such as $K_{\alpha}$ for L-shell to K-shell transitions and $K_{\beta}$ for M-shell to K-shell transitions, and the L-series, which involves transitions to the L-shell (n=2)
• For a tungsten (W) target, the $K_{\alpha}$ energy is 59.3 keV and the $K_{\beta}$ energy is 67.2 keV

X-ray interactions with matter

• Photoelectric effect occurs when an x-ray photon is completely absorbed by an atom, ejecting an electron
• Compton scattering involves an x-ray photon interacting with an outer shell electron, resulting in a scattered photon with reduced energy and an ejected electron

Medical Applications and Safety

X-rays in medical imaging

• Radiography (X-ray imaging) works by passing x-rays through the body, which are attenuated by tissues, with denser tissues like bones absorbing more x-rays and appearing lighter on the image, while less dense tissues like soft tissues absorb fewer x-rays and appear darker on the image
• Computed Tomography (CT) scans involve an x-ray tube and detectors rotating around the patient, taking multiple x-ray projections at different angles, which a computer then processes to create cross-sectional images and a 3D reconstruction of the body
• Contrast agents such as iodine or barium-based substances can be used to enhance the visibility of specific structures like blood vessels or the gastrointestinal tract
• The attenuation of x-rays in tissue is characterized by the absorption coefficient, which varies depending on the tissue type and x-ray energy

Safety and biological effects of x-rays

• X-rays are ionizing radiation that can ionize atoms and molecules in the body, potentially causing DNA damage and cell death
• Stochastic effects have a probability that increases with dose but no threshold dose, such as cancer risk
• Deterministic effects have a severity that increases with dose and a threshold dose, such as skin erythema and cataracts
• Dose reduction techniques include justification to ensure benefits outweigh risks, optimization following the ALARA principle (As Low As Reasonably Achievable), shielding with lead aprons, thyroid collars, and gonadal shields when appropriate, and collimation to restrict the x-ray beam to the area of interest
• Radiation protection principles involve minimizing exposure duration (time), maximizing distance from the source (distance), and using appropriate shielding materials (shielding)

Historical context and advancements

• Wilhelm Conrad Röntgen discovered x-rays in 1895, leading to significant advancements in medical imaging
• Modern x-ray detectors often use fluorescence to convert x-ray energy into visible light, which is then detected and processed to create digital images