In [Cr (C_{2}*O_{4}) 3 ]^ 3- , the isomerism shown is:

Key Ideas Needed

1. Bidentate Ligand:
   Oxalate, $C_2O_4^{2-}$, supplies two donor atoms (O and O) to the same metal, forming a 5-membered chelate ring.

2. Octahedral With Three Chelates:
   $[Cr(C_2O_4)_3]^{3-}$ contains three such ligands. Each ligand occupies two adjacent positions, giving a complete octahedron.

3. Types of Isomerism in Coordination Compounds

   • Structural (constitutional) – linkage, ionisation, coordination, hydrate, and ligand isomerism.
   • Stereoisomerism – geometrical (cis/trans, fac/mer) and optical (left-hand/ right-hand).

4. Conditions for Geometrical Isomerism:
   It appears only when there are different kinds of ligands in the same coordination sphere. Here all six positions are filled by the same bidentate ligand, so there is no geometrical variety.

5. Conditions for Optical Isomerism:
   An octahedral complex can be chiral if it lacks a plane/center of symmetry.
   • With three identical bidentate ligands ($[M(AA)_3]$ type), the complex forms two non-superimposable mirror images called Δ (delta) and Λ (lambda).

Hence, the only possible isomerism for $[Cr(C_2O_4)_3]^{3-}$ is optical isomerism.

Think of it like Lego® blocks around a ball

1. Metal Ball – Chromium (Cr) sits in the middle.
2. Three Double-Armed Lego Blocks – Each $C_2O_4^{2-}$ (oxalate) has two arms that grab the metal.
3. When you attach three of these double-armed blocks around the ball, you get something that can twist right-handed or left-handed, much like the blades of a fan.
4. Because the two twists are mirror images and can’t overlap, chemists call them optical isomers (they rotate light differently).

There are no other kinds (like ‘square vs. rectangle’ shapes) because all the blocks are identical – only the ‘handedness’ changes.

Step-by-Step Solution

1. Identify Ligand Type
   Oxalate ($C_2O_4^{2-}$) is bidentate, so three oxalate ions occupy all six coordination sites of the octahedral Cr(III) complex.

2. Check For Structural (constitutional) Isomers
   Linkage: impossible – oxalate coordinates through both oxygens only.
   Ionisation / hydrate / coordination: ligand set is fixed; not applicable here.
   Therefore no structural isomerism.

3. Check For Geometrical Isomers
   Geometrical variety (cis/trans, fac/mer) arises only with different ligands. Because all six donor atoms come from identical oxalate ligands, only one geometry exists ⇒ geometrical isomerism absent.

4. Check For Optical Isomers
   An octahedral $[M(AA)_3]$ complex has a propeller-like chiral arrangement. The two mirror images are labelled Δ and Λ. They cannot be superimposed.

   $\text{Thus } [Cr(C_2O_4)_3]^{3-} \text{ exhibits optical isomerism.}$

5. Answer
   The only isomerism shown is optical isomerism.