Paramagnetic Behavior in Cyano Complexes

To determine the cyano complex with the lowest value of paramagnetic behavior, we need to consider the electronic configurations of the metal ions and their coordination numbers.

Electronic Configurations of Metal Ions
- Cr (Z = 24): [Ar] 3d^5 4s^1
- Mn (Z = 25): [Ar] 3d^5 4s^2
- Fe (Z = 26): [Ar] 3d^6 4s^2
- Co (Z = 27): [Ar] 3d^7 4s^2

Coordination Numbers
The coordination number of a complex is the number of ligands bonded to the central metal ion. In this case, all the cyano complexes have a coordination number of 6, as indicated by the formula [M(CN)6]3-.

Analysis of Cyano Complexes
To determine the paramagnetic behavior of the cyano complexes, we need to consider the number of unpaired electrons in the metal ions. The presence of unpaired electrons leads to paramagnetic behavior.

- [Cr(CN)6]3-:
The electronic configuration of Cr3+ is [Ar] 3d^3. When it forms the complex [Cr(CN)6]3-, one electron from the 3d orbital is promoted to the 4s orbital, resulting in 4 unpaired electrons. Therefore, [Cr(CN)6]3- exhibits paramagnetic behavior.

- [Mn(CN)6]3-:
The electronic configuration of Mn3+ is [Ar] 3d^4. When it forms the complex [Mn(CN)6]3-, one electron from the 3d orbital is promoted to the 4s orbital, resulting in 5 unpaired electrons. Therefore, [Mn(CN)6]3- exhibits paramagnetic behavior.

- [Fe(CN)6]3-:
The electronic configuration of Fe3+ is [Ar] 3d^5. When it forms the complex [Fe(CN)6]3-, one electron from the 3d orbital is promoted to the 4s orbital, resulting in 4 unpaired electrons. Therefore, [Fe(CN)6]3- exhibits paramagnetic behavior.

- [Co(CN)6]3-:
The electronic configuration of Co3+ is [Ar] 3d^6. When it forms the complex [Co(CN)6]3-, all the 3d orbitals are filled, resulting in 0 unpaired electrons. Therefore, [Co(CN)6]3- exhibits diamagnetic behavior.

Conclusion
Among the given cyano complexes, [Co(CN)6]3- exhibits the lowest value of paramagnetic behavior as it has 0 unpaired electrons. Therefore, option A, [Co(CN)6]3-, is the correct answer.