Step 1: What chelation means.
A ligand carrying more than one donor site can grip the metal at two points at once, like a claw (Greek 'chele' = claw). The resulting five or six membered ring locks the metal in place. Complexes built from such chelating ligands resist dissociation more strongly than those built from single-site ligands, and this enhanced stability is the chelate effect.
Step 2: Illustration.
Compare \([Ni(en)_3]^{2+}\) with \([Ni(NH_3)_6]^{2+}\). Replacing six \(NH_3\) by three \(en\) molecules releases extra species into solution, raising the entropy; the more positive \(\Delta S\) lowers \(\Delta G\), so the chelated complex has a larger stability constant.
Step 3: Charge balance for the iron complex.
In \([Fe(CN)_6]^{4-}\) each cyanide is \(-1\), so iron must be \(+2\). Thus we treat \(Fe^{2+}\): \(3d^6\) after removing the two \(4s\) electrons.
Step 4: Pairing under a strong ligand.
\(CN^-\) lies high in the spectrochemical series, so the ligand field is large enough to pair the \(3d\) electrons. The \(d^6\) set collapses into three fully paired \(3d\) orbitals, vacating two \(3d\) orbitals for bonding.
Step 5: Orbital picture and prediction.
Two vacant \(3d\) + one \(4s\) + three \(4p\) mix into six equivalent \(d^2sp^3\) hybrids pointing to the corners of an octahedron. Each accepts a lone pair from \(CN^-\). Because it uses inner \(d\) orbitals it is a low-spin (inner orbital) octahedral complex, and with no unpaired electron it is diamagnetic.
\[ \boxed{d^2sp^3,\ \text{octahedral, inner orbital, diamagnetic}} \]