Match List-I with List-II and select the correct option.
Step 1: Analyze complexes and their coordination geometry
\([NiCl_4]^{2-}\) is a tetrahedral complex, typically with \(sp^3\) hybridization and a magnetic moment of 3.87 BM.
\([Ni(CN_4)]^{2-}\) is a square planar complex, usually with \(dsp^2\) hybridization and no unpaired electrons, resulting in a magnetic moment of 0 BM.
\([CoCl_4]^{2-}\) is an octahedral complex, typically with \(sp^3d^2\) hybridization and a magnetic moment of 2.82 BM.
\([Ni(H_2O)_6]^{2+}\) is a tetrahedral complex, exhibiting \(sp^3\) hybridization and a magnetic moment of 2.82 BM.
Step 2: Match complexes with characteristics
A.
\([NiCl_4]^{2-}\) matches with IV: \(sp^3\), tetrahedral, 3.87 BM.
B.
\([Ni(CN_4)]^{2-}\) matches with II: \(dsp^2\), square planar, 0 BM.
C.
\([CoCl_4]^{2-}\) matches with I: \(sp^3d^2\), octahedral, 2.82 BM.
D.
\([Ni(H_2O)_6]^{2+}\) matches with III: \(sp^3\), tetrahedral, 2.82 BM.
(b) If \( \vec{L} \) is the angular momentum of the electron, show that:
\[ \vec{\mu} = -\frac{e}{2m} \vec{L} \]