Hund’s rule and

C08-0030. Write brief explanations of (a) screening (b) the Pauli exclusion principle (c) the aufbau principle (d) Hund s rule and (e) valence electrons. 

In general, linear 7r-electron systems with Z1r = 2N electrons at the lowest energy levels have closed-shell singlet states while cyclic systems reach closed shell structures only when ZT = 4N + 2. Cyclic 7r-electron systems with Zn 4N + 2 will therefore exhibit multiplet ground states according to Hund s rules, and should be chemically reactive because of the unpaired electrons. Hiickel s rule that predicts pronounced stability for so-called aromatic ring systems with 4jV + 2 7r-electrons is based on this shell structure. The comparison with cyclic systems further predicts that ring closure of linear 7r-electron systems should be exothermic by an amount... 

We write the orbital diagram of each element following Hund s rule and count the number of unpaired electrons. 

In order to assign the four quantum numbers for a particular electron, first begin with the electron in the lowest energy level, n = 1. Assign the value of n, then the corresponding values of /, mh and finally ms. Once you have finished all the possible electrons at n = 1, repeat the procedure with n = 2. Don t forget about Hund s rule and the Pauli exclusion principle. The quantum numbers for the six electrons in carbon would be ... 

The treatment of atoms with more than one electron (polyelectronic atoms) requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number (the spin quantum number) which specifies the intrinsic energy of the electron in any orbital. The restriction on numbers of atomic orbitals and the number of electrons that they can contain leads to a discussion of the Pauli exclusion principle, Hund s rules and the aufbau principle. All these considerations are necessary to allow the construction of the modern form of the periodic classification of the elements. 

In this section, in discussing a typical antiferromagnetic crystal like MnO, we suppose as indicated in the last section that each Mn2 + ion has a moment due to its five electrons lined up by Hund s rule, and that the crystal is an insulator. 

If each of the six n electrons in benzene occupied a single atomic n orbital and there were no interaction, each would have an energy of a. The total energy would then be 6a, which is zero if we assume, as above, that a is the zero of our energy scale. However, when the atomic orbitals interact to produce the MOs, the six electrons will now occupy these MOs according to Hund s rule and the Pauli exclusion principle. The first two will enter the A orbital, and the remaining four occupy the E orbitals. The total energy of the system is then... 

Electrons within a subshell for which l > 0 tend to avoid pairing within the same orbital. This rule is Hund s rule and reflects the relatively greater electrostatic repulsion between two electrons in the same orbital as compared with occupancy of two orbitals having differing values for mi. 

Follow Hund s rule and the Pauli exclusion principle to fill the box-diagram with the remaining electrons. 

Atomic and ionic energy levels are characterized by a term symbol of the general form 25+1L/. The values of S, L, and J of lanthanide ions Ln3+ in the ground state can be deduced from the arrangement of the electrons in the 4f subshell, which are determined by Hund s rules and listed in Table 18.1.4. 

Knowing these three rules—the Aufbau principle, the Pauli exclusion principle, and Hund s rule—and the energy levels of the orbitals shown in Figure 2.4, it is possible to predict the electron configurations of most atoms. And these configurations are one of the keys needed to unlock the secrets of the chemical bond. 

So how is an electron configuration written First, the number of total electrons must be determined. This is the equal to the mass number for neutral atoms. For ions, the total electron is corrected for the charge (add electrons for anions subtract electrons for cations). The electrons are added according to Hund s rule and the Aufbau principle. Figure 10.3 describes the order in which the electrons are added. Keep in mind the maximum number of electrons in each type of orbital s orbitals hold two electrons, p orbitals hold six electrons, d orbitals hold ten electrons, and f orbitals hold 14 electrons. 

Finally, it must be stressed that Hund s rules (and indeed the whole L-S coupling picture) do not generally apply well to heavy atoms. However, magnetic measurements confirm their approximate validity in the transition series Sc to Fe. The occupation of the 3d and 4s orbitals is indicated in the following scheme ... 

Thinking Critically Use Hund s rule and orbital diagrams to describe the sequence in which ten electrons occupy the five orbitals related to an atom s d sublevel. 

The Jahn-Teller effect overrides Hund s rule and the ground state of the Cgg molecules is a singlet with a low lying excited triplet state [18,51] (Fig. 3). Thus NaiCeo is nonmagnetic [51]. 

Place the appropriate number of electrons in the molecular orbital energy levels by first determining the total number of valence electrons in the molecule or ion and then placing these in the molecular orbitals, starting with the lowest energy MO. Hund s rule and the Pauli exclusion principle should be followed. 

Your molecular orbital diagram should look like figure 2.18 which shows the MO diagram for Period 2 homonuclear diatomic molecules from Li2 to N2. Each carbon atom has four valence electrons, thus a total of 8 electrons has to be placed in the molecular orbitals on the diagram. Keep in mind that you still follow the Hund s rule and the Pauling exclusion principle when filling molecular orbitals with electrons. See the solution for E2.22... 

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