The haexaaquamanganese (II) ion contains five unpaired electrons, while the hexacyano ion contains only one unpaired electron. Expalin using crystal field theory.

Explanation

Because of the presence of six ligands the complex os octahedral and thus, d-orbital split up into lower energy `t_(2g)` orbitals and higher energy `e_(g)` orbitals.
`CN^(-)` is a strong field ligand (thus, causes pairing) and `H_(2)O` is a weak field ligand. Mn (II) ion has `3d^(5)` configuration. In the presence of `H_(2)O` molecules (acting as weak field ligand), the distributiion of these five electrons is `t_(2g)^(3),e_(g)^(2)`, i.e. all the electrons remain unpaired to form a high spin complex.

However in the presence of `CN^(-)` (acting as strong field ligands), the distribution of these eelctrons is `t_(2g)^(5),e_(g)^(0)`, i.e. two `t_(2g)` orbitals conatin paired eelctrons
while the third `t_(2g)` orbital contains one unpaired eelctron. The complex formed is a low spin complex.