Basic Atomic Structure

The classically described structure of an atom is known as the Bohr atom. It depicts a set of electrons orbiting the nucleus in stable electron shells (K, L, M, N) (Fig. 20-1). Each of the shells represents an energy state, with the innermost shell (K) associated with the greatest potential energy. Each electron’s energy state is defined further by a discrete set of four quantum numbers per electron. The Pauli exclusion principle states that no two electrons in the same atom can have an identical set of quantum numbers. By definition, a stable atom exists in its lowest possible energy state. When the energy state of an electron is increased (i.e., moved to a higher energy orbital shell or via absorption of external energy), the electron emits energy spontaneously as it returns to its lower, more stable energy state. This emission of energy by unstable electrons provides one mechanism for radionuclide imaging and is described in detail in the next section.

FIGURE 20-1 Model of the Bohr atom. The Bohr atom predicts an atomic model where the nucleus is surrounded by electron shells.

Electrons orbit a nucleus composed of a dense conglomerate of protons and neutrons that are bound together by a network of so-called strong nuclear forces. A proton contains a charge of 1.6 × 10⁻¹⁹ coulombs, which is the exact opposite charge of an electron. Neutrons are particles of slightly greater mass than protons, but are uncharged. The number of protons present in its nucleus, or Z number, defines each element, whereas the mass number, or A, represents the number of protons plus the number of neutrons. Specific nomenclature defines the relationship between the number of protons and neutrons in a nucleus (Table 20-1). The ratio of protons to neutrons defines the stability of a particular nucleus (Fig. 20-2); the transformation of an unstable nucleus to a more stable state is responsible for many of the radioactive emissions used in nuclear imaging.

TABLE 20-1 Nuclear Nomenclature

FIGURE 20-2 Nuclear stability. The ratio of protons to neutrons in a nucleus defines its stability and potential for radioactive decay. The line of stability diverges from the line of identity (equal proton/neutron ratio) at higher N numbers.

Radioactivity: Electron Transition, Unstable Nuclei, and Radioactive Decay

Radiation refers to the transfer of energy across distance, and can be in the form of kinetic energy transfer through the interaction of charged particles or through electromagnetic energy transfer in the form of photons. Our discussion focuses primarily on the physics of electromagnetic/photon radiation because this is the most relevant to cardiac nuclear imaging. A photon is a massless, chargeless carrier of energy that behaves much like a wave, traveling at the speed of light. Photons generated from energy transitions occurring in the electron cloud are termed x-rays, and photons emitted from nuclear transitions are termed gamma rays.

The energy (E) transmitted by a photon is proportional to its wavelength (λ, in nm). Because photons travel at the speed of light (c), the energy carried by a photon (in keV) is governed by the equation:

Photons released from different radionuclides have different wavelengths and different energies. The characteristic energy (or energies) of photons released from different radionuclides plays a crucial role in image generation (photopeak generation) and in the creation of imaging artifacts (e.g., attenuation, scatter).

Radiation can involve energy contained either in electrons or in the nucleus. An electron of a particular element exists in a characteristic energy state defined by its unique quantum number. This energy is a combination of the kinetic energy of motion of the electron and potential energy between the electron and the charges contained within the nucleus. The strength of this potential energy is proportional to the number of protons in the nucleus, and is inversely proportional to the distance of the electron from the nucleus. A heavy element (i.e., large Z number) with many protons exerts more force on an orbital electron and has more potential energy, and an inner shell electron has greater potential energy than an outer shell electron. This potential energy is commonly referred to as the binding energy for that electron and represents the energy required to separate that electron from the atom. With the introduction of energy equal to its binding energy, an electron can be removed from an atom with a resulting orbital electron vacancy. This process is called ionization. In contrast to ionization, if the energy transmitted to the orbital electron is insufficient to remove it from its shell, the transferred energy is dissipated as heat in a process known as excitation.

Two types of ionization electron transition can occur. In heavy elements (elements with a high number of protons, or Z number), a characteristic x-ray is produced when an electron from an outer shell fills an inner shell vacancy (Fig. 20-3). The energy difference between two electron shells is characteristic of the element, given the different Z number and nuclear charge that define that element. The energy released as the characteristic x-ray represents the difference in potential energy between the outer shell electron and its new quantum state in the inner shell. The movement of an electron from an outer shell to an inner shell produces an x-ray with a characteristic energy, which can be described as a K, L, M, or N x-ray, and the energy of a characteristic x-ray from a particular element can be predicted based on the subatomic structure of the element. An example of a characteristic x-ray emission is the 68- to 70-keV mercury characteristic x-ray that is emitted from thallium 201.

FIGURE 20-3 Examples of electron transition. Characteristic x-rays (top) and Auger electrons (bottom) can be emitted during electron transition.

Another mechanism of electron transition that leads to energy emission occurs when an outer shell electron fills an inner shell vacancy, but transfers the energy difference to an outer shell orbital electron (rather than emitting a characteristic x-ray), leading to the emission of an Auger electron (see Fig. 20-3). Because the release of an Auger electron leads to an orbital vacancy, a cascade of subsequent characteristic x-rays or further Auger electrons can occur after the initial emission. Auger electrons are usually produced when orbital electron vacancies are filled in elements of low Z number.

Besides energy transfer involving electrons, energy can also be released from the nucleus. Unstable nuclei can release energy in an attempt to reach a more stable energy state through the process of radioactive decay. This process is also called nuclear transformation. Radioactive decay of a particular unstable nucleus can occur in a series of decay steps, involving one or more of the types of radioactive decay described subsequently. Molybdenum-99 decays by β⁻ emission (discussed in detail later) to Tc 99m. Tc 99m undergoes subsequent gamma emission by isomeric transition producing the stable daughter Tc 99m. The “m” notation refers to a metastable excited nucleus with a measurable life span before its decay (approximately 10⁻¹² seconds), which is an intermediate between the “excited” and “stable” states.

Radioactive decay can involve particulate and nonparticulate emissions. Different types of radioactive decay are described in Table 20-2 and include alpha particle emission, beta particle emission, positron emission, electron capture, gamma ray emission, and internal conversion.

Alpha particles are equivalent to a He nucleus (two protons, two neutrons). Alpha particles are massive in size compared with other particulate emissions, and because of their large size cannot travel far in matter before an interaction occurs, and their energy is released. Because alpha particles cannot travel significant distances, their use in imaging is limited. The much higher linear energy transfer of alpha particles compared with beta particles or gamma photons results in significantly greater effective doses of absorbed radiation.

Beta particle emission occurs when a nucleus is unstable because of an elevated neutron/proton ratio (Fig. 20-4). When this occurs, a neutron is converted to a proton with the emission of an electron (β⁻) and an antineutrino (υ⁻). Because of the ejection of the electron and antineutrino from the nucleus, the daughter has an atomic number that is one greater than the parent. This decreases the instability generated by the elevated number of neutrons.

FIGURE 20-4 Nuclear emissions. Examples of nuclear emissions include beta particle emissions (β⁻), positron emissions (β⁺), and electron capture. υ, neutrino, υ⁻, antineutrino.

In contrast to beta particle (β⁻) emission, when a nucleus is unstable because of an increased number of protons, radioactive decay can occur through positron emission (β⁺) or electron capture (see Fig. 20-4). A positron, which is effectively an electron with a positive charge, is emitted during times of proton excess with the simultaneous generation of a neutron. When a positron is emitted from the nucleus, it quickly encounters an electron in the environment, leading to the annihilation of both particles. This annihilation event converts all of the mass of the two particles into energy, with the subsequent generation of two photons of equal energy that travel at 180 degrees to each other. Because the total energy generated by the annihilation reaction is 1.02 MeV, each of the photons emitted from the reaction carries an energy of 511 keV. The high energy of these photons and their simultaneous generation allowing for coincidence detection underlie the mechanisms for positron emission tomography (PET).

A separate process by which a proton-rich nucleus can obtain nuclear stability is through electron capture (see Fig. 20-4). In electron capture, an inner shell electron combines with a nuclear proton to form a neutron, creating a more stable nucleus. An outer shell electron fills the vacant inner shell with the subsequent generation of characteristic x-rays or Auger electrons. Positron emission and electron capture are competitive processes, with β⁺ emission occurring more frequently in “lighter” elements, and electron capture occurring in “heavier” elements. The characteristic x-rays that are produced during thallium 201 decay (described previously) are produced through electron capture.

Gamma ray emission occurs during nuclear transformation when the process of radioactive decay does not completely dissipate the energy required for the atom to reach its most stable state. Gamma rays are a form of electromagnetic radiation with variable energy without mass or charge (i.e., a photon). Gamma rays carry off the excess nuclear energy through the process of isomeric transition. Isomeric transition occurs when a metastable nucleus is present from a prior radioactive decay. This can commonly occur after β⁻ decay, but can also occur as a consequence of internal conversion (see Fig. 20-4), where an unstable nucleus transfers its energy to an inner shell (K or L) electron, leading to its expulsion as a conversion electron. An outer shell electron, releasing energy via a characteristic x-ray or Auger electron, fills the subsequent electron vacancy. The ability of gamma rays to penetrate tissue (and be used as an imaging tool) depends on their energy. An example of isomeric transition is the gamma photon emitted from the decay of the metastable Tc 99m nucleus.

Radioactive Decay