Monday, February 25, 2019

coordination compounds - Why isn't the orbital angular momentum also considered while calculating the magnetic moments 3d transition elements?


My textbook (Chapter: The d- and f- Block Elements) makes an interesting assertion, however, without any reason to back it up.




Paramagnetism arises from the presence of unpaired electons, each such electron having a magnetic moment associated with its spin angular momentum and orbital angular momentum. For the compounds of the first series of transition metals, the contribution of the orbital angular momentum is effectively quenched and hence is of no significance. For these, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the ‘spin-only’ formula, i.e.,


$$\mu = \sqrt{n (n + 2)}$$


where $n$ is the number of unpaired electrons and $\mu$ is the magnetic moment in units of Bohr magneton (BM). A single unpaired electron has a magnetic moment of $1.73$ Bohr magnetons (BM).



Now from what I've learnt from my physics classes last week, the magnetic moment of an electron is calculated using the formula:



$$\frac{m}{L} = \frac{e}{2 m_e}$$


Magnetic moment of revolving electron,


$$m = \frac{e}{2 m_e}L$$


In vector form,



$$\vec{m} = - \frac{e}{2m_e}\vec{L}$$



Where $m$ is the mass of the electron, $e$ is the magnitude of charge associated with the electron and $L$ is the angular momentum of the electron.


Now as I understand it, the angular momentum of an electron in an atom is the resultant of the electron's spin angular momentum and its orbital angular momentum.


But (as you can clearly see) my textbook exhibits an unexplained enthusiasm for only the spin angular momentum. It dismisses the contribution of the orbital angular momentum, as inconsequential, when determining the magnetic moments of electrons in the 3d elements.


As for the 'reason' provided by my textbook:



For the compounds of the first series of transition metals, the contribution of the orbital angular momentum is effectively quenched and is hence of no significance.



Well, I fail to see how that even counts as a 'reason'. I did ask my teacher about this, but she expressed her reluctance to go into the details; she's of the opinion that my particular query is “not worth clarifying” since it has no significance from the examination point of view (“Just give them what's in the textbook Aaron, nothing more and certainly not anything less”).



Subsequent internet searches have not yield any satisfying explanation (Perhaps I didn't use the right keywords while searching?).


So I'll just break up my question, point-wise, and list them below:




  1. Is the orbital angular really of no significance when calculating the magnetic dipole moment for 3d elements? If it is significant, is there any 'educational' purpose behind that omission in my textbook, or is it just a mistake?




  2. (As stated in the book) What causes the 'quenching'? How is this 'quenching' effect caused?





  3. Do the transition elements of the other periods also have "insignificant" orbital angular momentum contributions? Is it for the same reason as the 3d transition elements.






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