Subshells orbitals and

The electronic configuration of an atom describes the number of electrons that an atom possesses, and the orbitals in which these electrons are placed. The arrangements of electrons in orbitals, subshells and shells are called electronic configurations. Electronic configurations can be represented by using noble gas symbols to show some of the inner electrons, or by using Lewis structures in which the valence electrons are represented by dots. 

The arrangement of electrons into orbitals, subshells, and shells provides an explanation for the similarities in chemical properties of various elements, h Table 3.2 gives the number of electrons in each shell for the first 20 elements of the periodic table. 

A new concept is often made easier to understand by relating it to something familiar. The concept of electronic configurations is very likely new to you, but you are probably familiar with hotels. The way electrons fill up orbitals, subshells, and shells around a nucleus can be compared to the way rooms, floors, and hotels located near a convention center will fill with convention delegates. To make our analogy work, imagine that the hotels are located on a street that runs uphill from the convention center, as shown. Further imagine that none of the hotels has elevators, so the only way to get to upper floors is to climb the stairs. 

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. 

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 / in an atom are said to be in the same subshell. (Electrons having the same values of n, /, and m in an atom are said to be in the same orbital.) Thus, the first two electrons of magnesium (Table 17-3) are in the first shell and also in the same subshell. The third and fourth electrons are in the same shell and subshell with each other. They are also in the same shell with the next six electrons (all have n = 2) but a different subshell (/ = 0 rather than 1). With the letter designations of Sec. 17.3, the first two electrons of magnesium are in the Is subshell, the next two electrons arc in the 2s subshell, and the next six electrons are in the 2p subshell. The last two electrons occupy the 3s subshell. 

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

Electrons are located in major energy levels called shells. Shells are divided into subshells, and there are orbitals for each subshell. 

Electrons fill the orbitals in order of increasing energy, meaning that the lowest energy subshells are filled first. This is known as the aufbau principle. Of course, some subshells, such as the p subshell and the d subshell, have degenerate orbitals. 

As you can see, carbon has two half-filled orbitals in the 2p subshell and, at first sight, it might have been expected to form two covalent bonds rather than the four. So why does carbon form four covalent bonds ... 

There will be two electrons in the s subshell, six electrons in the p subshell and 10 electrons in the d subshell, which means that there must be 14 electrons in the f subshell. Therefore there must be seven f orbitals to accommodate these 14 electrons. 

The third shell or energy level is M and may contain a maximum of 18 electrons its orbital is called the d subshell, and it may have a maximum of 10 electrons for example,... 

A set of orbitals with the same values n and 1 is called a subshell and is represented by notation like 2/) (See Figure 4-1.)... 

The electronic configuration of carbon atom is Is, 2s2, 2p. Is and 2s form the completed subshell and hence do not contribute towards the total angular momentum. Only the two electrons in the p orbitals need be cousidered. For p electrons, J — t. Hence, l = l,/2 = 1. 

In general two electrons, with opposed spins, may occupy each atomic orbital. There is one s orbital in each electron shell, with a given value of the total quantum number n three p orbitals, corresponding to mi = — 1, 0, and +1, in each shell beginning with the L shell five d orbitals in each shell beginning with the M shell, and so on. The numbers of electrons in completed subshells and shells of an atom are shown in Table 2-3. Note that there are alternative ways of naming the shells. 

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

Carbon has only two electrons in its 2p subshell and can readily accept another in its vacant 2pz orbital. Nitrogen, however, has a half-filled 2p subshell, and the additional electron must pair up in a 2p orbital, where it feels a repulsion from the electron already present. Thus, the Eea of nitrogen is less favorable than that of carbon. Oxygen... 

Principal quantum number A number (n = 1, 2, 3,. ..) that describes the location of an electron shell (energy level) around the nucleus of an atom (compare with orbital, shell, and subshell). 

If we examine the electrons of a lone carbon atom in its ground state we would see that its four valence electrons are in their expected atomic orbitals, two in the orbital of the subshell and two in orbitals of the p subshell. The p electrons are at a higher energy state than the electrons. 

Linear complexes where the central atom (e.g. Cu(I), Ag(I) or Au(I)) has a d10 configuration follow a 14-electron rule. Here, the o bonding can be described by using sp hybrids, so that two np orbitals on the central atom can be regarded as out of action, and we require 14 electrons to fill up the d subshell and provide for two bonds. 

The subshells and the types of orbitals for the first four energy levels (principle quantum numbers) are shown below. 

Ceulemans considers a dn electron state, split by an octahedral field into the e and t2 levels, so that all the n electrons are in the t2 subshell. In the notation of Sugano et al. [27], rjj(t2SrMsMr) is the multi-electronic wavefunction, with SMs irrep labels for the total spin and rMr irrep labels in the octahedral group for the orbital state. We use a real orbital basis in which all njm factors take their simplest possible forms and suppress S, r and Mr below. It takes six electrons (three pairs each of opposed spin) to fill this t2 subshell. Ceulemans [7] particle-hole conjugation operator 0() has the effect of conjugating the occupancies within this subshell, and of... 

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