A practical review of basic atomic and nuclear physics is essential to understand the origins of radiations, as well as their interactions with matter. The nature and type of emissions are determined by the structural character of the atom and nucleus. The ways in which radiation interacts with matter have a direct relationship with imaging and radiation safety. The types of radiation and how they interact with matter are the foundation of radionuclide imaging and radiation safety. This chapter will focus on atomic and nuclear structure and the interaction of radiations with matter as they relate to radionuclide imaging.

Matter is composed of atoms and the characteristics of a specific form of matter are determined by the number and type of atoms that make it up. How atoms combine is a function of their electron structure. The electron structure is determined by the nuclear architecture. As we have yet to image the atom, its structure is based on a “most-probable” model that fits physical behaviors we observe. The probabilistic approach is based on the model of the atom proposed by Niels Bohr in 1913. The Bohr atom proposed a positively charged nucleus, surrounded by negatively charged electrons. A neutral atom is one in which the positive and negative charges are matched. A mismatch in these charges determines the ionic character of the atom, which is the basis for its chemistry. The electron configuration is also a source for emissions used in radionuclide imaging.

These emissions, or radiations, may be in either of the two forms: particulate or electromagnetic. The origins of either type of radiation may be from the nucleus or the electron structure.

Electron Configuration

Electrons are arranged around the nucleus in shells. The number of shells is determined by the number of electrons, which is, in turn, determined by the number of protons in the nucleus. The force exerted on these shells, called binding energy, is determined by the proximity of the shell to the nucleus. Higher binding energies are exerted on shells closest to the nucleus and conversely, lower binding energy for those more distant from the nucleus. The innermost shell is named the “K” shell and electrons in this shell are subject to the highest binding energy. The magnitude of that energy is dependent on the positive forces, which is determined by the number of protons in the nucleus. The shells more distant from the nucleus are named L, M, N, and so on. Each of these shells has lower binding energies as a result of their distance from the nucleus (Fig. 1-1).

The radii of each of these shells increase as a function of their distance from the nucleus. An expression of this is given by assigning an integer value (1, 2, 3, …) to each shell. The lower values represent smaller radii. These integer values are called quantum numbers. Therefore, the K shell has a quantum number of 1, L = 2, M = 3, etc. This pattern continues until all available electrons are bound to a shell. The innermost shells are filled with electrons preferentially. The maximum number of electrons is specific to each shell and is calculated by 2n², where n is the quantum number. Therefore, the maximum number of electrons for each shell is:

These shells are further subdivided into substates. The number of substates for each shell can be calculated by 2n – 1; therefore:

Each substate for a given shell will have a unique binding energy. For instance, the L shell has 3 substates, L_I, L_II, and L_III.¹ Each of these has slightly different distances from the nucleus, and therefore slightly different binding energies (Fig. 1-2).²

Atomic Radiations

Electrons in inner shells being under high binding energy and thus tightly bound to the nucleus are in an inherently low-energy state. Outer shell and free electrons are in an inherently higher-energy state. Therefore, to move an inner shell electron to an outer shell requires energy. The amount of energy required is simply the difference between binding energies.

Example: Binding energy for a hypothetical “K” shell = 100 keV and “L” = 50 keV. K₁₀₀ – L₅₀ = 50 keV of energy input to move the electron.

Conversely, the movement of an electron from an outer shell to an inner shell, L → K, yields energy. This energy yield results in the emission of radiation. The energy of the radiation is equal to the differences in binding energies of the shells. The radiation may take on two different forms: characteristic x-ray or Auger (oh-zhay) effect.

Example: Binding energy for a hypothetical “K” shell = 100 keV and “L” = 50 keV. K₁₀₀ – L₅₀ = 50 keV of energy given to the electron.

Characteristic x-rays are electromagnetic radiations (photons) that are created when an outer shell electron moves to fill an inner shell vacancy. This vacancy may occur for several reasons—to be discussed later. The energy of this photon is equal to the difference between binding energies. Since binding energies are determined by, or characteristic of, the number of protons in the nucleus, and it is the number of protons that determines an element’s identity, the characteristic x-ray energies are specific to each element and the electron shells from which they originate. X-radiation is defined as an electromagnetic radiation originating outside the nucleus, therefore the term characteristic x-ray.

The Auger effect occurs under the same conditions as characteristic x-ray, that is, an inner shell vacancy being filled by an outer shell electron. The difference is that the excess energy from the cascading electron is radiated to another electron. This ejects that electron from its shell. This free electron will have kinetic energy equal to the difference in the binding energies less the binding energy of the shell of the free electron. The Auger effect is more common in elements with lower numbers of protons (Z number).^1–3

Nuclear Structure

The nucleus is composed mainly of neutrons and protons. Any particle contributing to the structure of the nucleus is called a nucleon. The conventional nomenclature to describe the nucleons is: .

The total mass of an atom is essentially the combined masses of the nucleons. Electrons contribute less than 1% to the total mass.¹

Nuclides having the same number of protons (Z number) are called isotopes. Isotopes may exhibit different atomic masses (A number) and therefore have different numbers of neutrons (N number). Nuclides with the same N are called isotones and will be different elements, since the Z numbers are different. Nuclides with the same A number are called isobars and different elements as well.

Isotopes having different N numbers are of particular interest to imagers because they have the same chemistry, since their Z numbers and, therefore, electron numbers are the same.^1–5 Some isotopes exhibit the emission of radiations, which is due to the differences in the number of neutrons. These isotopes are called unstable. If all the stable isotopes of all elements are plotted, comparing proton number to neutron number, a pattern emerges as illustrated in Figure 1-3.

Elements with low Z numbers have proton to neutron ratios that are 1:1. As Z numbers increase, this ratio increases to as high as 1.5. This distribution of stable elements is called the line of stability. By definition, an element with a proton to neutron ratio that falls to either the left or right of the line of line of stability is unstable. The unstable isotopes, radioisotopes, are unstable because their nuclear configurations are either proton rich or neutron rich relative to stable configurations. These radioactive elements seek stability by undergoing transformations in their nuclear configurations to a more stable P ↔ N ratio. The type of transformation will be a result of P ↔ N ratio, that is, proton rich versus neutron rich. This type of transition is called the mode of decay.^1–4

Modes of Decay

The goal of nuclear decay is to equate the balance of forces in the nucleus. The repelling forces originating from the positive charge (coulombic forces) of the protons, when matched by the attractive forces from within the nucleus (exchange forces), define stability. When these forces are mismatched, nuclear transformations (radioactive decay) result. The mode of decay will produce unique emissions and lead to a more stable nuclear configuration. In radionuclide imaging, the ideal mode of decay would result in a high yield of photons, at an energy that is efficiently detected by our imaging instrumentation. Photon emission is also desirable from the radiation safety and dosimetry perspectives, due to their lower probability of creating potentially damaging interactions as compared to particles. With these considerations, it is important to understand the modes of decay of ^99mTechnetium, ²⁰¹Thallium, and ⁸²Rubidium—the most commonly used radionuclides used in nuclear cardiology.^1,2,6

BETA⁻ Decay

In an unstable nuclear configuration where the nucleus is neutron rich, β⁻ decay occurs. To decrease the neutron–proton ratio, a neutron is converted to a proton and an energized electron is emitted. The expression of this nuclear transition is:

where n is the neutron, p the proton, e the electron, and ν the neutrino.

The neutrino (ν) behaves like a particle with no mass and is not critical to imaging considerations. The primary emission is the energized electron (e⁻). The nuclear configuration that results from β⁻ decay is a daughter with a stable or more stable energy state and an additional proton in its nucleus.

Example:

Since the number of protons is changed, the elemental identity changes. This is called a transmutation. The daughter atomic mass (X) remains the same as the parent nucleus, and the energy carried off by the ejected electron called transition energy. This leads to a more balanced relationship of coulombic force (repelling forces due to the protons) and exchange force (attractive nuclear forces). The resulting emission of the energized electron, a β⁻ particle, is of no use in imaging and contributes to an increase in radiation dose in a biologic system. This decay process may lead to a daughter that is not fully stable, but more stable than the parent.^1,2

BETA⁺ Decay

In nuclear configurations where the parent is proton rich, β⁺ decay may occur. In this mode of decay, a proton is converted to a neutron and the emission of an energized, positively charged electron (β⁺) results. The nuclear equation is:

The energy of the β⁺ particle contributes to resolving the transition energy between the unstable parent and more stable daughter, as in β⁻ decay.

An important secondary emission will result from the formation of the β⁺ particle. Since there is an abundance of negatively charged electrons in nature, the resulting positively charged electron (β⁺) will be attracted to, and collide with, a free negatively charged electron. This collision results in the annihilation of both particles. The annihilation leads to the conversion of the mass of these particles to their equivalent energy state. This is expressed by Einstein’s equation E = mc², where E is energy, m the mass, and c the speed of light. This essentially states that energy and mass are simply two physical forms of the same thing. Therefore, two photons (E) are emitted, each with the energy equivalent to the mass (m) of an electron, which is 511 keV. Unique to this annihilation is that these photons are emitted in a 180-degree trajectory from each other. It is these photons that are detected and registered into an image in positron imaging. The change in nuclear configuration is a decrease in Z and increase in N.