Which of the following complexes will show jahn-Teller distortion?

Options

A. `[Cu(H_2O)_6]^(2+)`
B. `[Cr(H_2O)_6]^(3+)`
C. `[Mn(H_2O)_6]^(2+)`
D. `[Co(H_2O)_6]^(3+)`

Answer

To determine which of the given complexes will show Jahn-Teller distortion, we need to analyze the electronic configurations of the central metal ions in each complex and how the electrons are distributed in the d-orbitals.

### Step-by-Step Solution:

1. **Understanding Jahn-Teller Distortion**:
- Jahn-Teller distortion occurs in octahedral complexes where there is an unequal distribution of electrons between the t2g and eg orbitals. This usually happens when the d-orbital configuration is either d9 or d7 (in certain cases).

2. **Analyzing the First Complex: Cu(H2O)6^2+**:
- Copper (Cu) has an atomic number of 29. In the +2 oxidation state, its electronic configuration is 3d^9.
- In an octahedral field, the d-orbitals split into t2g (lower energy) and eg (higher energy) sets.
- For Cu^2+ (3d^9), the electron distribution will be:
- t2g: 6 electrons (fully filled)
- eg: 3 electrons (unsymmetrical distribution)
- Since there is an unequal distribution of electrons, this complex will show Jahn-Teller distortion.

3. **Analyzing the Second Complex: Cr(H2O)6^3+**:
- Chromium (Cr) has an atomic number of 24. In the +3 oxidation state, its electronic configuration is 3d^3.
- For Cr^3+ (3d^3), the electron distribution will be:
- t2g: 3 electrons (fully filled)
- eg: 0 electrons
- This distribution is symmetrical, so this complex will not show Jahn-Teller distortion.

4. **Analyzing the Third Complex: Mn(H2O)6^2+**:
- Manganese (Mn) has an atomic number of 25. In the +2 oxidation state, its electronic configuration is 3d^5.
- For Mn^2+ (3d^5), the electron distribution will be:
- t2g: 3 electrons
- eg: 2 electrons
- This distribution is symmetrical, so this complex will not show Jahn-Teller distortion.

5. **Analyzing the Fourth Complex: Co(H2O)6^3+**:
- Cobalt (Co) has an atomic number of 27. In the +3 oxidation state, its electronic configuration is 3d^6.
- For Co^3+ (3d^6), and considering H2O is a strong field ligand, the electron distribution will be:
- t2g: 6 electrons (fully filled)
- eg: 0 electrons
- This distribution is symmetrical, so this complex will not show Jahn-Teller distortion.

### Conclusion:
From the analysis, the only complex that shows Jahn-Teller distortion is **Cu(H2O)6^2+** due to its unsymmetrical distribution of electrons in the eg orbitals.