Subshells example

Form cations with complete, typically unreactive c/-subshells Example Ga, [Ar] 45 3d ° 4p gallium(lll), Ga [Ar] 3d °... 

This problem clearly did not worry Stoner, who just went ahead and assumed that three quantum numbers could be specified in many-electron atoms. In any case, Stoner s scheme solved certain problems present in Bohr s configurations. For example, Bohr had assigned phosphorus the configuration 2,4,4,41, but this failed to explain the fact that phosphorus shows valencies of three and five. Stoner s configuration for phosphorus was 2,2,2,4,2,2,1, which easily explains the valencies, since it becomes plausible that either the two or the three outermost subshells of electrons form bonds. 

There are 2/ + 1 different values of trij for a given value of / and therefore 2/ + 1 orbitals in a subshell of quantum number /. For example, when / = 1, mj= +1,0, — 1 so there are three p-orbitals in a given shell. Alternatively, we can say that a subshell with / = 1 consists of three orbitals. 

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... 

In the d block, the energies of the (n — l )d-orbitals lie below those of the ns-orbitals. Therefore, the ws-electrons are lost first, followed by a variable number of (n — 1 )d-electrons. For example, to obtain the configuration of the Fe3+ ion, we start from the configuration of the Fe atom, which is [Ar]3d 64s2, and remove three electrons from it. The first two electrons removed are 4s-electrons. The third electron comes from the Id-subshell, giving [Ar 3d5. 

The shell number is represented by 1, 2, 3, and so forth, and the letters designate the subshells. The superscript numbers tell how many electrons occupy each subshell. Thus, in this example, there are two electrons in the Is subshell, two electrons in the 2s subshell, six electrons in the 2p subshell, and only one electron in the 3s subshell. (The 3s subshell can hold a maximum of two electrons, but in this atom this subshell is not filled.) The total number of electrons in the atom can easily be determined by adding the numbers in all the subshells, that is, by adding all the superscripts. For sodium, this sum is 11, equal to the atomic number of sodium. 

It turns out that fully filled or half-filled subshells have added stability compared with subshells having some other numbers of electrons. One effect of this added stability is the fact that some elements do not follow the n +1 rule exactly. For example, copper would be expected to have a configuration... 

The principal characteristic of the transition elements is an incomplete electronic subshell that confers specific properties on the metal concerned. Ligand systems may participate in coordination not only by electron donation to the 3d levels in the first transition series but also by donation to incomplete outer 4s and 4p shells. Figure 5.1 shows that the differences in orbital energy levels between the 4s, 4p and 3d orbitals are much smaller than, for example, the difference between the inner 2s and 2p levels. Consequently, transitions between the 4s, 4p and 3d levels can easily take place and coordination is readily achieved. The manner in which ligand groups are oriented in surrounding the central metal atom is determined by the number and energy levels of the electrons in the incomplete subshells. 

Each shell contains one or more subshells, each with one or more orbitals. The second quantum number is the angular momentum quantum number (/) that describes the shape of the orbitals. Its value is related to the principle quantum number and has allowed values of 0 to (n-1). For example, if n = 4, then the possible values of / would be 0,1, 2, and 3 (= 4-1). 

According to the latest atomic model, the electrons in an atom are located in various energy levels or shells that are located at different distances from the nucleus. The lower the number of the shell, the closer to the nucleus the electrons are found. Within the shells, the electrons are grouped in subshells of slightly different energies. The number associated with the shell is equal to the number of subshells found at that energy level. For example, energy... 

For example, lithium has an electron arrangement 2,1, but its electronic configuration is Is 2s. The characters in red indicate the shell and subshell. The numbers in blue indicate the number of electrons in that subshell. So the two electrons in the first shell of lithium atoms are located in the Is subshell or Is orbital. The one electron in lithium s second shell is in the 2s subshell or 2s orbital. Now consider carbon. It has the electron arrangement 2, 4. The two electrons in the first shell go into the Is orbital. The next subshell to be filled is the 2s orbital, which holds a maximum of two electrons. The remaining two electrons go into the next available subshell, which is 2p. So carbon has an electronic configuration Is 2s 2pl... 

This can be explained in terms of the relative stability of different electronic configurations and thus provides evidence for these electronic configurations. To help you understand this, you have to appreciate that there is a special stability associated with a filled subshell or a half-filled subshell - for example, the p subshell when it contains three or six electrons. Likewise, the d subshell is most stable when it contains five or ten electrons. The more stable the electronic configuration, then the more difficult it is to remove an electron and therefore the ionisation energy is higher. 

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,... 

The anomalous electronic configuration of chromium and copper is interpreted as the displacement of 1 electron from an r orbital into a d orbital these 2 elements have only 1 electron in the As subshell because the second electron was promoted into a id subshell. This example warns you that there are exceptions to the general pattern of electronic configurations of... 

There is an important class of rearrangements of strained cyclic a-bonded systems to give less strained ir-bonded qrstems which occur under the influence of transition metal catalysts although the uncatalysed proce is Woodward-Hoffman forbidden and slow. Examples are the conversion of cubanes XXII and bis-homocubanes XXIll to syn-tricyclooctadienes XXIV and related species XXV and of quadricyclene (XXVI) to norbomadiene (XXVII) [Ag, however, converted cubane and related species to the previously unrecognised species cuneane (XXVIII) and its relatives as do some electrophiles with incompletely filled d-subshells ... 

Note carefully that each shell has been divided into a series of finer shells known as subshells. Each subshell corresponds to a specific orbital type. The four of the seventh shell, for example, includes the 7s orbital, the 5/orbitals, the 6z/orbitals, and the 7p orbitals. Gallium is larger than zinc because it has an electron in three subshells of the fourth shell, while zinc has electrons only in the first inner two subshells of the fourth shell. Thus, what you see here is a refinement on the model presented in Section 5.7. Don t worry about fully understanding this refinement. Rather, better that you understand that all conceptual models are subject to refinement. We chose the level of refinement that best suits our needs. 

The direct product is also useful for determining the symmetry of ip9l from the symmetry of the occupied MOs. For two nonequivalent electrons outside closed subshells, the symmetry species of el is given by the direct product of the species of the orbitals of the two electrons. For example, the first excited electronic configuration of H20 is... 

As an example take a gas in a cylindrical vessel. In addition to the energy there is one other constant of the motion the angular momentum around the cylinder axis. The 6A/-dimensional phase space is thereby reduced to subshells of 6N-2 dimensions. Consider a small sub volume in the vessel and let Y(t) be the number of molecules in it. According to III.2 Y(t) is a stochastic function, with range n = 0,1,2,. .., N. Each value Y = n delineates a phase cell ) one expects that Y(t) is a Markov process if the gas is sufficiently dilute and that pi is approximately a Poisson distribution if the subvolume is much smaller than the vessel. 

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