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With the help of CrT number of unpaired electron in a compound can be calculated and we can calculate its paramagnetic moment (due to spin only), by the formula:
\( \mu=\sqrt{n(n+2)} \) Bohr magneton (BM), where \( n \) is the number of unpaired electron in the complex.
For spectral analysis the separation between \( t_{2 g} \) and \( e_{g} \) orbitals, called ligand field splitting parameter \( \Delta_{0} \) (for octahedral complexes) should be known to us, which can be easily calculated by observing the absorption spectrum of one \( e^{-} \)complex figure shows the optical absorption spectrum of the \( \mathrm{d}^{1} \) hexaaquatitanium (III) ion \( \left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \). The CFT assigns the first absorption maximum at \( 20,300 \mathrm{~cm}^{-} 1 \) to the transition \( e_{\mathrm{q}} \leftarrow \mathrm{t}_{2 \mathrm{q}} \). For multielectronic \( \left(\mathrm{d}^{2}\right. \) to \( \left.\mathrm{d}^{10}\right) \) system, the calculation of \( \Delta_{0} \) by absorption spectrum is not that easy as the absorption spectrum will also be affected by electron-electron repulsions.
The magnetic moments of following, arranged in increasing order will be (atomic number of Co \( =27 \) )
(1) \( \mathrm{Co}^{3+} \) (octahedral complex with a strong field ligand)
(2) \( \mathrm{Co}^{3+} \) (octahedral complex with a weak field ligand)
(3) \( \mathrm{Co}^{2+} \) (tetrahedral complex)
(4) \( \mathrm{Co}^{2+} \) (square planar complex)
(A) \( 1234 \)
(B) \( 2341 \)
(C) \( 3241 \)
(D) \( 2431 \)
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