Shells, Subshells, and Orbitals

Electrons having the same value of n in an atom are said to be in the same shell. Electrons having the same value of n and the same value of I in an atom are said to be in the same subshell. (Electrons having the same values of n, I and mi in an atom are said to be in the same orbital.) Thus, the first two electrons of aluminum 

Since the possible numerical values of I depend on the value of n, the number of subshells within a given shell is determined by the value of n. The number of subshells within a given shell is merely the value of n, the shell number. Thus, the first shell has one subshell, the second shell has two subshells, and so forth. These facts are summarized in Table 4-4. Even the atoms with the most electrons do not have enough electrons to completely fill the highest shells shown. The subshells that hold electrons in the ground states of the biggest atoms are in boldface. 

Energy level n Type of Subshell Number of Subshells 

Show that there can be only two electrons in any subshell. 

For any given value of n, there can be a value of / = 0, corresponding to an subsheU. For 1 = 0 there can be only one possible m value nii = 0. Hence, n, /, and nii are all specified for a given subshell. Electrons can then have spin values of mj = -t- or mj = — j. Thus, every possible set of four quantum numbers is used, and there are no other possibilities in that subsheU. Each of the two electrons has the first three quantum numbers in common and has a different value of mj. The two electrons are said to be paired. 

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The hierarchy of shells, subshells, and orbitals is summarized in Fig. 1.30 and Table 1.3. Each possible combination of the three quantum numbers specifies an individual orbital. For example, an electron in the ground state of a hydrogen atom has the specification n = 1, / = 0, nij = 0. Because 1=0, the ground-state wavefunction is an example of an s-orbital and is denoted Is. Each... 

FIGURE 1.30 A summary of the arrangement of shells, subshells, and orbitals in an atom and the corresponding quantum numbers. Note that the quantum number m, is an alternative label for the individual orbitals in chemistry, it is more common to use x, y, and z instead, as shown in Figs. 1.36 through 1.38. 

FIGURE 1.41 The relative energies of the shells, subshells, and orbitals in a many-electron atom. Each of the boxes can hold at most two electrons. Note the change in the order of energies of the 3d- and 4s-orbitals after Z = 20. 

Table 5.2 Summary of Atomic Shell, Subshells, and Orbitals for Shells 1-4...

The hierarchy of shells, subshells, and orbitals is summarized in Fig. 1.22 and Table 1.3. Each possible combination of the three quantum... 

To understand the dual nature of light and the relationships among its energy, frequency, and wavelength 4.5 To write electronic configurations in a shorter notation, using the concepts of shells, subshells, and orbitals... 

I See the Saunders Interactive General Chemistry CD-ROM, Screen 7.11, Shells, Subshells, and Orbitals. 

Shells, Subshells, and Orbitals Orbital Shape Buildup Principle Electronic Structure and the Periodic Table Solved Problems... 

To help you get a better idea of this nested structure, the general characteristics of principal shells, subshells, and orbitals are described below. 

What is the relationship among principal shell, subshell, and orbital Use the n = 2 principal shell to show the relationships. 

Although it does not follow from the Schrodinger equation, there is a fourth quantum number, m that describes the spin of the electron. It can assume two values, -I-1/2 and —1/2. According to the Paufi Exclusion Principle no two electrons in an atom can have the same set of four quantum numbers. If two electrons have the same values for n (main shell), / (subshell), and (orbital), they must differ in spin. Each orbital in an atom can hold no more than two electrons, and they must be opposed in spin. Such a couple of electrons, opposite in spin, constitutes an electron pair. 

The electronic configurations described to this point provide details of the shells, subshells, and orbitals involved but are somewhat cumbersome. In some applications, these details are not needed, and simplified representations are used that emphasize the electrons in the valence shell. 

Niels Bohr proposed a theory for the electronic structure of hydrogen based on the idea that the electrons of atoms move around atomic nuclei in fixed circular orbits. Electrons change orbits only when they absorb or release energy. The Bohr model was modified as a result of continued research. It was found that precise Bohr orbits for electrons could not be determined. Instead, the energy and location of electrons could be specified in terms of shells, subshells, and orbitals, which are indicated by a notation system of numbers and letters. 

The modified Bohr model, or shell model, of electronic structure provides an explanation for the periodic law. The rules governing electron occupancy in shells, subshells, and orbitals result in a repeating pattern of valence-shell electron arrangements. Elements with similar chemical properties turn out to be elements with identical numbers and types of electfons in their valence shells. 

Table 16.1 shows the arrangement of shells, subshells, and orbitals in an atom. In the designation of an orbital. Is means n = 1 and / = 0 (an s subshell), 2p means n = 2 and / = 1 (a p subshell), and so forth. No more than two electrons can occupy any single orbital. An s subshell has only a single orbital, so its occupancy is also limited to two electrons. However, since a p subshell consists of three orbitals, a maximum of six electrons can occupy a p subshell. A d subshell consists of five orbitals, so it can be occupied by ten electrons. An f subshell has seven orbitals, so it can be occupied by fourteen electrons. In general, for a given value of I, there are 21+1 orbitals, and 2 times 21 + 1, or 4/ + 2, possible electrons. 

F ig U re 6.15 Illustration of how quantum numbers designate shells, subshells, and orbitals. 

Concerning the electrons in the shells, subshells, and orbitals of an atom, how many can have... 

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