Question

For the $t_{2g}^{6}e_{g}^{2}$ system, the value of magnetic moment ($\mu$) is:
a.) 2.83 BM
b.) 1.73 BM
c.) 3.87 BM
d.) 4.92 BM

Answer 1

Hint: Splitting of the crystal field is the difference in energy between ligand d orbitals. The number of the splitting of the crystal field is indicated by the capital Greek letter. The splitting of crystal fields describes the color difference between two identical metal-ligand complexes. The equivalent appears to increase with the amount of oxidation and increases the group on the standard table.

Complete step by step answer:
Crystal field theory (CFT) describes the breakdown of electron orbital state degenerations, typically d or f orbitals, due to a static electrical field generated by an anion neighbor. This theory was used to explain different spectroscopies of complexes of transition metal coordination, in particular optical spectra (colors). CFT effectively accounts for some of the transition metal complexes' magnetic properties, textures, hydration enthalpies, and spinel structures, but it does not try to explain bonding.
- The Crystal Field Stabilization Energy (CFSE) is the energy gain obtained by preferential electron filling of orbitals. Typically, it is smaller than or equal to 0. The complex is unstable when it is equal to 0. The magnitude of CFSE depends on the ligands' number and existence, and the complex's geometry.
- Consider octahedral ${{d}^{_{4}}}$ system. Three electrons are in lower ${{t}_{2g}}$ level. Fourth electron will enter into higher ${{e}_{g}}$ level if $\text{ }\!\!\Delta\!\!\text{ < P}$. Fourth electron will enter into lower ${{t}_{2g}}$​ level if $\text{ }\!\!\Delta\!\!\text{ > P}$. Here, P is the pairing energy. It is the energy required to pair two electrons against electron repulsion in the same orbital.
\[\begin{align}
 & {{e}_{g}}={{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{{{z}^{2}}}} \\
 & {{t}_{2g}}={{d}_{xy}},{{d}_{yz}},{{d}_{zx}} \\
\end{align}\]
- There are 6 electrons in ${{t}_{2g}}$ orbital and 2 electrons in ${{e}_{g}}$ orbital.
Therefore n = 2.
-Spin magnetic moment\[\mu =\sqrt{n\left( n+2 \right)}\] ,
Where, n = number of unpaired electrons.
Spin magnetic moment
\[\begin{align}
 & =\sqrt{n(n+2)} \\
 & =\sqrt{2(2+2)} \\
 & =\sqrt{8} \\
 & =2.83 \\
\end{align}\]
So, the correct answer is “Option A”.

Note: -In coordination complexes, magnetic moments are often used in combination with electronic spectra to gather information on the oxidation number and stereochemistry of the central metal ion.