Hybridisation of [Mn(CN)4]²-

The hybridisation of [Mn(CN)4]²- is dsp². This is because of the following reasons:

Determination of central atom:
In [Mn(CN)4]²-, Mn is the central atom as it forms the coordination bond with four CN ligands.

Electronic configuration of Mn:
The electronic configuration of Mn is [Ar] 3d5 4s2. In the ground state, the five d-orbitals are degenerate.

Hybridisation:
The hybridisation of Mn in [Mn(CN)4]²- can be determined using the following steps:

1. In the complex, Mn forms four sigma bonds with the four CN ligands using its four valence orbitals.

2. To form these bonds, one of the 4s electrons and three of the 3d electrons of Mn are promoted to the vacant 4p orbitals.

3. The hybridisation of Mn involves the mixing of one 4s, two 4p and one 3d orbitals to form four dsp² hybrid orbitals.

Explanation of dsp² hybridisation:
The dsp² hybridisation involves the following:

1. One 4s orbital, two 4p orbitals and one 3d orbital of Mn combine to form four dsp² hybrid orbitals.

2. Three of these orbitals are used to form sigma bonds with the three CN ligands lying in the same plane.

3. The fourth hybrid orbital is used to form a sigma bond with the CN ligand lying perpendicular to the plane of the other three CN ligands.

4. The two unhybridised 3d orbitals of Mn remain unused and contain one electron each.

Conclusion:
Thus, the hybridisation of [Mn(CN)4]²- is dsp² as a result of the mixing of one 4s, two 4p and one 3d orbitals of Mn to form four hybrid orbitals.