Quantum numbers missing

Find the values of the quantum numbers missing in each of the following situations. 

Of course, nowadays, as every student of chemistry and physics knows, electron orbits have been replaced by orbitals that are supposed to be smeared out in space. But this view misses the point somewhat and is not the whole lesson from quantum mechanics. The more radical lesson is that even these probability-based orbitals simply do not exist. The notion of assigning four quantum numbers to each electron is just an approximation, albeit a powerful one. 

Soon after Dennison had deduced from the specific-heat curve that ordinary hydrogen gas consists of a mixture of two types of molecule, the so-called ortho and para hydrogen, a similar state of affairs in the case of iodine gas was demonstrated by direct experiment by R. W. Wood and F. W. Loomis.1 In brief, these experimenters found that the iodine bands observed in fluorescence stimulated by white light differ from those in the fluorescence excited by the green mercury line X 5461, which happens to coincide with one of the iodine absorption lines. Half of the lines are missing in the latter case, only those being present which are due to transitions in which the rotational quantum number of the upper state is an even integer. In other words, in the fluorescence spectrum excited by X 5461 only those lines appear which are due to what we may provisionally call the ortho type of iodine molecule. 

The missing label % does not appear in the expression (4.57). One can convert Eq. (4.57) to the usual form by introducing the normal vibrational quantum numbers (Figure 4.7),... 

We have called the vibrational quantum numbers here Vj, v2, v3 in order to distinguish them from the local quantum numbers, va, vl , vc. Note that, in view of the presence of the missing label, %, the normal basis is not very convenient for calculations. The spectrum corresponding to Eq. (4.59) is shown in Figure 4.8. There are fewer examples of molecules for which the dynamical symmetry of the normal chain II, provides a realistic zeroth-order approximation. The normal behavior arises when the masses of the three atoms are comparable, as, for example in XY2 molecules with mx = mY. More examples are discussed in the following sections. 

O Fill in the missing values in the following sets of quantum numbers. 

The state of matters just described in the case of helium, viz. the -absence of the H/S-term, the expected ground state of the orthohelium term sequence, suggestedto Pauli (1925) a general examination of spectra, to see whether, in other elements and under other conditions, definite terms sometimes drop out. It was found that this actually happens moreover, the term analysis showed in all cases that in these missing terms all the quantum numbers of the electrons agreed. Conversely, it was also found, the terms always drop out when these quantum numbers are the same. This discovery led Pauli to the following principle ... 

The lower is the entropy of the intensity distribution, the more rapid is the increase of the cumulative probability.37 Figure 5 compares the results for two bands in2,38 C6D6 with the results for the distribution (2.17) at the same value of the total strength . For the band where quantum numbers can be assigned, each transition can be identified and no lines are missing, the cumulative distribution of the experimental results increases more rapidly than that for the most entropic intensity distribution. Not so for the band that is in the channel three region2 where intramolecular energy transfer is quite dominant. A similar behavior is found also for computational results.13 As a practical point, it is necessary to mention that for the purpose of this... 

FOLLOW-UP PROBLEM 7.6 Supply the missing quantum numbers and sub-level names. 

Roald Hoffmann has pointed out to us that the Bohr atom, a 2D model applied on the 3D world, works because the missing zero-point energy does cancel the wrong energy law of —(Z/ n — )), compared to —(Z/ny, for 2D and 3D, respectively. Note that the energy only depends on the principal quantum number, n = 1,2,3,... in both... 

This is clearly out for the transitional metals where the choice of principal quantum number (between s- or c/-orbitals) should be accompanied by atomic radii related information. This should be electronegativity, as a unique value (because the equalization of orbital electronegativities in atoms), to be involved as the missing information. 

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