What is the configuration of `Cr^(+3)` according to C.F.T.In aqueous medium?

Options

A. `t_(2g)^(2)e_(g)^(1)`
B. `t_(2g)^(3)e_(g)^(0)`
C. `t_(2g)^(1)e_(g)^(2)`
D. `t_(2g)^(0)e_(g)^(3)`

Answer

To determine the configuration of \( \text{Cr}^{+3} \) according to Crystal Field Theory (CFT) in an aqueous medium, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Oxidation State and Electron Configuration of Chromium:**
- Chromium (Cr) has an atomic number of 24. The electron configuration of neutral chromium is \( [Ar] 3d^5 4s^1 \).
- In the +3 oxidation state, chromium loses three electrons. The electrons are removed first from the 4s orbital and then from the 3d orbital. Therefore, the electron configuration for \( \text{Cr}^{+3} \) is:
\[ [Ar] 3d^3 \]

2. **Determine the Geometry of the Complex:**
- In an aqueous medium, chromium typically forms octahedral complexes due to the coordination number of 6.

3. **Understand Crystal Field Splitting in Octahedral Complexes:**
- In an octahedral field, the \( d \) orbitals split into two sets: the lower energy set \( t_{2g} \) (which has three orbitals) and the higher energy set \( e_g \) (which has two orbitals).
- The splitting pattern can be represented as:
\[ t_{2g} \quad \quad e_g \]

4. **Consider the Nature of the Ligand:**
- In this case, water (\( \text{H}_2\text{O} \)) acts as a ligand. Water is a weak field ligand, which means the splitting energy (\( \Delta \)) is relatively small.

5. **Fill the \( d \) Orbitals According to CFT:**
- For \( \text{Cr}^{+3} \) with a \( 3d^3 \) configuration, the electrons will fill the lower energy \( t_{2g} \) orbitals first before occupying the higher energy \( e_g \) orbitals.
- Thus, the filling will be:
- \( t_{2g} \): 3 electrons (fully filled)
- \( e_g \): 0 electrons
- Therefore, the configuration can be represented as:
\[ t_{2g}^3 \quad e_g^0 \]

6. **Conclusion:**
- The final configuration of \( \text{Cr}^{+3} \) in an aqueous medium according to CFT is:
\[ t_{2g}^3 \quad e_g^0 \]

### Final Answer:
The configuration of \( \text{Cr}^{+3} \) according to CFT in aqueous medium is \( t_{2g}^3 \, e_g^0 \).

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