To ascertain paramagnetism, the presence of unpaired electrons in the complex must be confirmed. Paramagnetic substances possess unpaired electrons, whereas diamagnetic substances have all electrons paired.
1. [NiCl\(_4\)]\(^{2-}\): Ni\(^2+\) has an electronic configuration of [Ar] 3d\(^8\). Within a tetrahedral field, characteristic of this complex, the Ni\(^2+\) ion exhibits unpaired electrons, rendering [NiCl\(_4\)]\(^{2-}\) paramagnetic.
2. Ni(CO)\(_4\): Carbon monoxide (CO) acts as a strong field ligand, inducing electron pairing in Ni, resulting in a diamagnetic complex. Consequently, Ni(CO)\(_4\) is diamagnetic.
3. [Ni(CN)\(_4\)]\(^{2-}\): The cyanide ion (CN\(^-\)) is a very strong field ligand, causing the pairing of electrons in Ni\(^2+\).
Therefore, [Ni(CN)\(_4\)]\(^{2-}\) is diamagnetic.
4. [Ni(H\(_2\)O)\(_6\)]\(^{2+}\): Water (H\(_2\)O) functions as a weak field ligand. In a weak field ligand environment, Ni\(^2+\) (d\(^8\)) retains unpaired electrons, making [Ni(H\(_2\(_2\)O)\(_6\)]\(^{2+}\) paramagnetic.
5. Ni(PPh\(_3\))\(_4\): Triphenylphosphine (PPh\(_3\)) is a weak field ligand. In this environment, Ni\(^2+\) will possess unpaired electrons, classifying Ni(PPh\(_3\))\(_4\) as paramagnetic.
Accordingly, the correct designation is (3) A, D, and E only.