By J. E. Spice and J. E. Spice (Auth.)
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Extra resources for Chemical Binding and Structure
Clearly, then, the net magnetic moment becomes less, as the temperature increases. A detailed analysis shows the magnetic moment induced in one mole of material to be: ,Z = Np2H/3kT,where p is the permanent magnetic moment (in Bohr magnetons) per molecule. The molar paramagnetic susceptibility is the ratio between this and the field strength, namely, xp = Np2/3kT, and should therefore vary inversely with the absolute temperature. This is found to be so for gases, liquids, and many solids. For some other solids there is a slightly more complicated relationship.
Here, however, is an important difference, through the 4 / l e v e l having virtually the same energy as the 5d and the 6s. After one electron has entered the 5d level, the next fourteen are accommo dated in the 4/, and it is only when this sub-level is full that the 5d sub-level is completed. In this period there is therefore a series of fourteen elements, all with three incomplete electron-shells, which are known as the rare-earth or lanthanide elements. F o r the second long period and for this very long period, the normal filling of s and ρ levels takes place before and after the various transition series.
According to the quantum theory, the unit of angular momentum is h/2n9 so that the unit magnetic moment should be eßmcxhßn, or ehjAnmc. According to wave mechanics, the total orbital angular momentum of an electron is > / [ / ( / + 1 ) ] . h/2n, where / is the subsidiary quantum number, so that the orbital magnetic moment should be > / [ / ( / + 1 ) ] . eh/4nmec9 where e is now the electronic charge, and me is the mass of an electron. Experi ment confirms this prediction. The constant eh/4nmec = μ09 is called the Bohr magneton.