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Figure 1.6 K, L, and M electron shells.

       Quantum numbers:

The atomic electrons in their shells are usually described by their quantum numbers, of which there are four types. The first is the principal quantum number (n), which identifies the shell. The first three shells (K, L, and M) are depicted in Figure 1.6. The electron binding energy is greatest for the innermost shell (K) and is progressively less for the outer shells. Larger atoms have more shells.

      The second (azimuthal), third (magnetic), and fourth (spin) quantum numbers refer to other physical properties of the electron. Each electron within an atom has a unique combination of the four quantum numbers.

      The maximum number of electrons associated with each energy shell is 2n², where n is the shell number. The first shell (the K shell) can contain a maximum of two electrons, the second shell (the L shell) can contain a maximum of eight electrons, the third shell (the M shell) can contain a maximum of 18 electrons, and so on.

       Representation of electron distribution:

      Most of the diagrams (for example Figure 1.6) in this chapter reflect what is referred to as the Bohr model of the atom and as such all electrons within each shell are depicted as moving along the surface of a sphere, each shell represented as one such sphere with a distinct radial distance from a centrally located nucleus. The radius of these spheres increases with principal quantum number. This model of the atom is frequently used for teaching purposes because the radial distance of an electron from the nucleus is used to depict with how tightly bound it is to the atom—the closest electrons being most tightly bound.

A more accurate quantum mechanical description of electron distribution uses a sequence of orbitals. Orbitals are mathematical functions that describe the probability of finding an electron in a region of space near the nucleus. For each principal quantum number (each shell) there is a spherical orbital denoted by the principal quantum number followed by the letter “s”. This orbital contains two electrons (Figure 1.7a). This is the only orbital for the K shell which contains at maximum two electrons and this orbital is called the 1s orbital. The neutral atom with a full K shell is the helium atom.

      The next shell, the L shell (n = 2), also has a spherical orbital, denoted 2s (also depicted as Figure 1.7a) which contains two electrons, as well as three sub‐orbitals, denoted 2p_x, 2p_y, 2p_z. Each sub‐orbital has a shape like a dumb‐bell or three‐dimensional figure eight (see Figure 1.7b). The three sub‐orbitals are oriented along three orthogonal axes as shown in Figure 1.7c. Each sub‐orbital is filled by two electrons and the neutral atom with completely filled orbitals for n = 1 and n = 2 is Neon.

      For the higher order orbitals, n > 2, the sub‐orbitals associated with higher azimuthal quantum number become even more complicated in structure and will not be discussed here.

      Quantum numbers

      The term quantum means, literally, amount. It acquired its special significance in physics when Bohr and others theorized that physical quantities such as energy and light could not have a range of values as on a continuum, but rather could have only discrete, step‐like values. The individual steps are so small that their existence escaped the notice of physicists until Bohr postulated them to explain his theory of the atom. We now refer to Bohr’s theory as quantum theory and the resulting explanations of motion in the atomic scale as quantum mechanics to distinguish it from the classical mechanics described by Isaac Newton, which is still needed for everyday engineering.

Figure 1.7 Electron orbitals and sub‐orbitals. (a) s orbital, (b) p suborbital, (c) p suborbitals, p_x, p_y, p_z.

       Stable electron configuration:

      Just as it takes energy to remove an electron from its atom, it takes energy to move an electron from an inner shell to an outer shell, which can also be thought of as the energy required to pull a negative electron away from the positively charged nucleus. Any vacancy in an inner shell creates an unstable condition often referred to as an excited state.

      The electrical charges of the atom are balanced, that is, the total negative charge of the electrons equals the total positive charge of the nucleus. This is simply another way of pointing out that the number of orbital electrons equals the number of nuclear protons. Furthermore, the electrons must fill the shells with the highest binding energy first. At least in the elements of low atomic number, electrons within the inner shells have the highest binding energy.

      If the arrangement of the electrons in the shells is not in the stable state, they will undergo rearrangement in order to become stable, a process often referred to as de‐excitation. Because the stable configuration of the shells always has less energy than any unstable configuration, the de‐excitation releases energy as X‐rays and electrons (this will be discussed in more detail later in this chapter in the section on internal conversion).

       Nucleus

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