Number of unpaired electrons in [Fe(dipy)3]2

To determine the number of unpaired electrons in [Fe(dipy)3]2, we need to analyze the electronic configuration of the central iron (Fe) atom.

Electronic configuration of Fe
The atomic number of Fe is 26, which means it has 26 electrons. The electronic configuration of Fe can be written as 1s2 2s2 2p6 3s2 3p6 4s2 3d6.

Dipyridyl (dipy) ligand
The dipyridyl (dipy) ligand is a bidentate ligand, which means it can form two coordination bonds with the central metal atom. Each dipy ligand contributes two electrons to the coordination complex.

Coordination complex [Fe(dipy)3]2
In [Fe(dipy)3]2, there are three dipy ligands attached to the central Fe atom. Each dipy ligand donates two electrons to the Fe atom for coordination bond formation. Therefore, a total of six electrons are contributed by the dipy ligands.

Calculating the number of unpaired electrons
To determine the number of unpaired electrons, we need to consider the electronic configuration of Fe after the coordination bond formation. In this case, Fe has a d6 electron configuration (3d6).

Hund's rule
According to Hund's rule, electrons occupy separate orbitals of the same energy before pairing up in an orbital. This principle applies to the d orbitals as well.

Explanation
Since the d6 configuration allows for the possibility of pairing up of electrons in the d orbitals, we need to consider the ligand field splitting of the d orbitals to determine if any of the electrons are unpaired.

In the case of [Fe(dipy)3]2, the dipy ligands cause a ligand field splitting, which results in the d orbitals splitting into two sets of energy levels - the lower energy t2g set (dxy, dxz, dyz) and the higher energy eg set (dx2-y2, dz2).

Electron pairing and unpaired electrons
Since there are no electrons in the eg set and the t2g set can accommodate a maximum of six electrons, all six electrons from the dipy ligands can be accommodated in the t2g set without any electron pairing. This means that all the electrons in the t2g set are paired, resulting in zero unpaired electrons.

Conclusion
The number of unpaired electrons in [Fe(dipy)3]2 is 0.