Number of unpaired electrons in the complex [Ag(CN)2]- are '0'

Explanation:

1. Coordination Complex:
A coordination complex consists of a central metal ion or atom surrounded by ligands, which are typically ions or molecules that donate electron pairs to the metal ion to form coordinate bonds.

2. Structure of [Ag(CN)2]-:
The complex [Ag(CN)2]- consists of a central silver ion (Ag+) surrounded by two cyanide ligands (CN-). The cyanide ligands act as monodentate ligands, meaning they donate one electron pair to the metal ion.

3. Ligand Field Theory:
In the context of coordination complexes, Ligand Field Theory is used to describe the splitting of d orbitals of the central metal ion in the presence of ligands. This splitting leads to the formation of energy levels known as d-orbitals.

4. Crystal Field Theory:
Crystal Field Theory is a simplified version of Ligand Field Theory that assumes point charges instead of molecular orbitals. According to Crystal Field Theory, the d-orbitals of the central metal ion are split into two sets of different energies: the lower energy set, or the t2g set (dxy, dxz, dyz), and the higher energy set, or the eg set (dx2-y2, dz2).

5. Electron Configuration of Ag+:
The electron configuration of Ag+ is [Kr] 4d10. Since Ag+ loses one electron to form the complex, the electron configuration of the central silver ion in [Ag(CN)2]- becomes [Kr] 4d9.

6. Hund's Rule:
Hund's Rule states that electrons occupy degenerate orbitals singly before pairing up. This means that in the presence of ligands, the electrons will first fill the lower energy t2g set before occupying the higher energy eg set.

7. Filling of d-orbitals in [Ag(CN)2]-:
In [Ag(CN)2]-, the 4d orbitals of the central silver ion are split into t2g and eg sets. Since Ag+ has 9 electrons in its 4d orbitals, they will occupy all three t2g orbitals singly before pairing up. Therefore, there are no unpaired electrons in the complex [Ag(CN)2]-.

Conclusion:
The complex [Ag(CN)2]- has '0' unpaired electrons.