Step 1: Understanding the Organometallic Compounds and their Characteristics.
- (A) Fe(C\(_5\)H\(_5\))\(_2\): This is a ferrocene compound, where iron is sandwiched between two cyclopentadienyl anions. The metal in this complex undergoes dsp\(^2\) hybridization.
- (B) K\(^+\)[PtCl\(_3\)(C\(_2\)H\(_4\))]: This complex has a tetramer structure, which means it is composed of four monomeric units.
- (C) Mg(CH\(_3\))\(_2\): This is an organomagnesium compound, and such compounds exhibit fluxionality, where the ligands may interchange positions.
- (D) (CH\(_3\))\(_2\)AlF\(_4\): This complex is polymeric in nature due to the bonding between the metal center and the ligands forming extended chains or networks.
Step 2: Conclusion.
Thus, the correct matching is:
- (A) - (I): Fe(C\(_5\)H\(_5\))\(_2\) undergoes dsp\(^2\) hybridization.
- (B) - (II): K\(^+\)[PtCl\(_3\)(C\(_2\)H\(_4\))] has a tetramer structure.
- (C) - (III): Mg(CH\(_3\))\(_2\) exhibits fluxionality.
- (D) - (IV): (CH\(_3\))\(_2\)AlF\(_4\) is polymeric in nature.
Therefore, the correct answer is option (2).
Number of carbon atoms connected to the metal center in [W(C\(_{60}\))(CO)\(_5\)] is _________ (rounded off to the nearest integer).
(Given: atomic number of W = 74)
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: