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Which of the following complex compounds will exhibit highest paramagnetic behaviour? (At. No. Ti = 22, Cr = 24, Co = 27, Zn = 30)
A
$[Co(NH_3)_6]^{3+}$
B
$[Zn(NH_3)_6]^{2+}$
C
$[Ti(NH_3)_6]^{3+}$
D
$[Cr(NH_3)_6]^{3+}$
Detailed Solution
Paramagnetism increases with the number of unpaired electrons: $\mu = \sqrt{n(n + 2)}$ BM.
$[Co(NH_3)_6]^{3+}$: $Co^{3+}$ is $3d^6$; $NH_3$ causes pairing here ($t_{2g}^6$, inner orbital $d^2sp^3$ complex), so there are 0 unpaired electrons (diamagnetic).
$[Zn(NH_3)_6]^{2+}$: $Zn^{2+}$ is $3d^{10}$, 0 unpaired electrons (diamagnetic).
$[Ti(NH_3)_6]^{3+}$: $Ti^{3+}$ is $3d^1$, 1 unpaired electron.
$[Cr(NH_3)_6]^{3+}$: $Cr^{3+}$ is $3d^3$ ($t_{2g}^3$), 3 unpaired electrons.
Hence $[Cr(NH_3)_6]^{3+}$ shows the highest paramagnetic behaviour.
$[Co(NH_3)_6]^{3+}$: $Co^{3+}$ is $3d^6$; $NH_3$ causes pairing here ($t_{2g}^6$, inner orbital $d^2sp^3$ complex), so there are 0 unpaired electrons (diamagnetic).
$[Zn(NH_3)_6]^{2+}$: $Zn^{2+}$ is $3d^{10}$, 0 unpaired electrons (diamagnetic).
$[Ti(NH_3)_6]^{3+}$: $Ti^{3+}$ is $3d^1$, 1 unpaired electron.
$[Cr(NH_3)_6]^{3+}$: $Cr^{3+}$ is $3d^3$ ($t_{2g}^3$), 3 unpaired electrons.
Hence $[Cr(NH_3)_6]^{3+}$ shows the highest paramagnetic behaviour.