Hund first rule

Strategy First (1) find the total number of electrons (Z Co = 27). Then (2) find the electron configuration the first 18 electrons form the argon core, and the remaining electrons enter the 3d sublevel. Finally (3) apply Hund s rule to obtain the orbital diagram. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

Hund s first rule The ground term will be one of maximum spin-multiplicity (maximum S)... 

To minimize electron-electron repulsion, put three of the 3 p electrons in different orbitals, all with the same spin, and then place the fourth electron, with opposite spin, in the first orbital. In accord with Hund s rule, this gives the same value of JHj to all electrons that are not paired. Here is the energy level diagram for the valence 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 ... 

Assume that the exclusion principle and Hund s rule are followed. Demonstrate that the periodic table for the first 30 elements would be as shown below ... 

Hund s rule establishes that all orbitals of a given sublevel must have been occupied by single electrons with parallel spins before two electrons of opposite spins can occupy a single sublevel. Let us consider, for instance, a metallic ion with configuration. Based on Hund s rule, the first three electrons occupy the l2g degenerate orbitals with parallel spins. The remaining two electrons then have two possibilities ... 

Hund s rule explains that when degenerate orbitals (orbitals that have same energy) are present but not enough electrons are available to fill all the shell completely, then a single electron will occupy an empty orbital first before it will pair up with another electron. This is understandable, as it takes energy to pair up electrons. Therefore, the six electrons in the carbon atom are filled as follows the first four electrons will go to the Is and 2s orbitals, a fifth electron goes to the 2px, the sixth electron to the 2py orbital and the 2p orbital will remain empty. 

We first note that an isolated atom with an odd number of electrons will necessarily have a magnetic moment. In this book we discuss mainly moments on impurity centres (donors) in semiconductors, which carry one electron, and also the d-shells of transitional-metal ions in compounds, which often carry several In the latter case coupling by Hund s rule will line up all the spins parallel to one another, unless prevented from doing so by crystal-field splitting. Hund s-rule coupling arises because, if a pair of electrons in different orbital states have an antisymmetrical orbital wave function, this wave function vanishes where r12=0 and so the positive contribution to the energy from the term e2/r12 is less than for the symmetrical state. The antisymmetrical orbital state implies a symmetrical spin state, and thus parallel spins and a spin triplet. The two-electron orbital functions of electrons in states with one-electron wave functions a(x) and b(x) are, to first order,... 

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... 

The ground state of carbon presents a new problem Which orbital does the sixth electron go into This question can be answered by doing either an experiment or a calculation. The answers are summarized in Hund s first rule ... 

The second step is called Hund s rule, for the German spectroscopist Friedrich Hund, who first proposed it. This procedure gives the configuration of the atom that corresponds to the lowest total energy, taking into... 

Assuming that g orbitals fill according to Hund s rule, what is the atomic number of the first element to have a filled g orbital ... 

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