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Electrons are enigmatic entities, with properties of both particles and wave energy, that move very rapidly around the nucleus in ultimately unpredictable paths. Our depiction of the electron cloud is based on the probabilities of finding a particular electron at a particular place. The wave‐like properties of electrons help to define the three‐dimensional shapes of their probable locations, known as orbitals. The size and shape of the electron cloud defines the chemical behavior of atoms and ultimately the composition of all the Earth materials they combine to form. Simplified models of the electron cloud depict electrons distributed in spherical orbits around the nucleus (Figure 2.3); the reality is much more complex. Because the electron cloud largely determines the chemical behavior of atoms and how they combine to produce Earth materials, it is essential to understand some fundamental concepts about it.

Figure 2.3 Distribution of electrons in the principal quantum levels (“electron shells”) of uranium: K‐shell electrons violet; L‐shell blue; M‐shell bluish green; N‐shell green; O‐shell yellow; P‐shell orange and Q‐shell red.

Every electron in an atom possesses a unique set of properties that distinguishes it from all the other electrons in that atom. An individual electron's identity is given by four properties that include its (1) principal quantum number, (2) azimuthal quantum number, (3) magnetic quantum number, and (4) spin number. Each electron in the electron cloud possesses a unique combination of the four quantum properties.

The principal quantum number (n) signifies the principal quantum energy region, sometimes called “level” or “shell ” in which a particular electron occurs. It is related to its distance from the nucleus. Principle quantum regions are numbered in order of increasing electron energies 1, 2, 3, 4, 5, 6 or 7 or alternatively lettered K, L, M, N, O, P or Q. These are arranged from low principal quantum number for low energy regions closer to the nucleus to progressively higher quantum number for higher energy regions farther away from the nucleus.

Each principal quantum region or level contains electrons with one or more azimuthal or angular momentum quantum numbers which signify the directional quantum energy region, sometimes called “subshell ”, in which the electron occurs. This is related to the angular momentum of the electron and the shape of its orbital. Azimuthal quantum numbers or subshells are labeled s, p, d, and f. As discussed below, the number of electrons in the s and p “subshells” of the atom's highest principal quantum level largely determines the chemical behavior of elements. All four azimuthal quantum numbers are important for understanding the layout of the periodic table of the elements which is discussed below. The other two quantum properties, the magnetic quantum number (m) and the spin number (±½) define the orientation of the quantum probability region in which the electron is located and its spin relative to a reference framework. Table 2.2 summarizes the quantum properties of the electrons that can exist in principle quantum regions or “shells” 1–7. To summarize, each electron in an atom possesses a unique set of the four principle quantum properties.

Atomic nuclei were created largely during the “big bang,” by subsequent fusion reactions between protons and neutrons in the interior of stars, and in supernova. When elements are formed, electrons are added to the lowest available quantum level in numbers equal to the number of protons in the nucleus. Electrons are added to the atoms in a distinct sequence, from lowest quantum level electrons to highest quantum level electrons. The relative quantum energy of each electron is shown in Figure 2.4.

Table 2.2 Quantum designations of electrons in the 92 naturally occurring elements. The numbers refer to the principal quantum region occupied by the electrons within the electron cloud; small case letters refer to the subshell occupied by the electrons.

Principal quantum number	Subshell description	Number of electrons
1 (K)	1s	2
2 (L)	2s	2
2p	6
3 (M)	3s	2
3p	6
3d	10
4 (N)	4s	2
4p	6
4d	10
4f	14
5 (O)	5s	2
5p	6
5d	10
5f	14
6 (P)	6s	2
6p	6
7 (Q)	7s	2
	Total = 92

Figure 2.4 The quantum properties of electrons in the 92 naturally occurring elements, listed with increasing quantum energy (E) from bottom to top; K‐shell electrons violet; L‐shell blue; M‐shell bluish green; N‐shell green; O‐shell yellow; P‐shell orange and Q‐shell red.

The diagonal rule is a simple rule or memory device that predicts, with very few exceptions, the sequence in which electrons are added to the electron cloud. The order in which electrons are added to shells is depicted by a series of diagonal lines from 1s to 7p (Figure 2.5).

Table 2.3 shows the ground state electron configurations for the elements. One can write the electron configuration of any element in a sequence from lowest to highest energy electrons. For example, calcium (Z = 20) possesses the electron configuration 1s₂, 2s₂, 2p₆, 3s₂, 3p₆, 4s₂. Elements with principal quantum levels (shells) or azimuthal quantum s‐ and p‐subshells that are completely filled (that is they contain the maximum number of electrons possible) possess very stable electron configurations. These elements include the noble gas elements such as helium (He), neon (Ne), argon (Ar), and krypton (Kr) which, because of their stable configurations, tend not to react with or bond to other elements. For elements other than helium, the highest quantum level stable configuration is s2, p₆, sometimes referred to as the “stable octet. ”

Figure 2.5 The diagonal rule for determining the sequence in which electrons are added to the electron cloud; K‐shell electrons violet; L‐shell blue; M‐shell bluish green; N‐shell green; O‐shell yellow; P‐shell orange and Q‐shell red.