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 1: Determine the electron configuration of neutral chromium (Cr)
- Chromium (Cr) has an atomic number of 24.
- The electron configuration of neutral chromium is:
\[ \text{Cr}: [\text{Ar}] \, 4s^1 \, 3d^5 \]
Here, the 4s subshell is filled before the 3d subshell.

### Step 2: Remove electrons to form \( \text{Cr}^{3+} \)
- To form \( \text{Cr}^{3+} \), we need to remove 3 electrons from the neutral chromium configuration.
- The electrons are removed first from the 4s subshell and then from the 3d subshell.
- Therefore, the removal of electrons proceeds as follows:
- Remove 1 electron from \( 4s^1 \) → \( 4s^0 \)
- Remove 2 electrons from \( 3d^5 \) → \( 3d^3 \)

### Step 3: Write the electron configuration of \( \text{Cr}^{3+} \)
- After removing the electrons, the electron configuration of \( \text{Cr}^{3+} \) becomes:
\[ \text{Cr}^{3+}: [\text{Ar}] \, 3d^3 \]

### Step 4: Analyze the crystal field splitting in an octahedral field
- In an octahedral field, the \( 3d \) orbitals split into two sets: \( t_{2g} \) and \( e_g \).
- The \( t_{2g} \) set is lower in energy and can hold a maximum of 6 electrons, while the \( e_g \) set is higher in energy and can also hold a maximum of 6 electrons.

### Step 5: Distribute the electrons in the split orbitals
- Since \( \text{Cr}^{3+} \) has 3 electrons in the \( 3d \) subshell, these electrons will fill the lower energy \( t_{2g} \) orbitals first.
- The filling of the orbitals will be as follows:
- All three electrons will occupy the \( t_{2g} \) orbitals, leading to:
\[ t_{2g}^3 \, e_g^0 \]

### Final Answer
- The configuration of \( \text{Cr}^{3+} \) in an octahedral field according to CFT is:
\[ t_{2g}^3 \, e_g^0 \]