`[Cr(H_2 O)_6]Cl_3` (at no. of Cr = 24) has a magnetic moment of `3.83 B.M`. The correct distribution of `3d` electrons the chromium of the complex.

Options

A. `3d_(xy)^(1) , 3d_(yz)^(1) , 3 d_(zx)^(1)`
B. `3d_(xy)^(1) , 3d_(yz)^(1) , 3d_(z^(2))^(1)`
C. `3d_((x^(2) - y^(2)))^(1) , 3d_(z^(2))^(1) , 3d_(xz)^(1)`
D. `3d_(xy)^(1) , 3d_((x^(2)- y^(2)))^(1) , 3d_(yz)^(1)`

Explanation

To determine the correct distribution of 3d electrons in the chromium complex `[Cr(H2O)6]Cl3`, we need to follow these steps:

### Step 1: Determine the oxidation state of chromium in the complex.
In the complex `[Cr(H2O)6]Cl3`, water (H2O) is a neutral ligand, and chloride (Cl) has a charge of -1. Since there are three chloride ions, the total negative charge contributed by the chlorides is -3. To balance this, chromium must have an oxidation state of +3.

### Step 2: Find the electronic configuration of chromium.
The atomic number of chromium (Cr) is 24. The ground state electronic configuration of chromium is:
\[ \text{Cr: } [Ar] 3d^5 4s^1 \]

### Step 3: Adjust the electronic configuration for the oxidation state.
Since chromium is in the +3 oxidation state in this complex, we remove three electrons. The electrons are removed first from the 4s orbital and then from the 3d orbital:
- Remove 1 electron from 4s: \( 3d^5 4s^0 \) becomes \( 3d^4 \)
- Remove 2 electrons from 3d: \( 3d^4 \) becomes \( 3d^3 \)

Thus, the electronic configuration for Cr in the +3 state is:
\[ \text{Cr}^{3+}: [Ar] 3d^3 \]

### Step 4: Determine the number of unpaired electrons.
In the \( 3d^3 \) configuration, there are three electrons in the 3d orbitals. Since water is a weak field ligand, it does not cause pairing of the electrons. Therefore, all three electrons will remain unpaired.

### Step 5: Write the distribution of the 3d electrons.
The distribution of the three unpaired electrons in the \( 3d \) orbitals can be represented as follows:
- \( 3d_{xy}^1 \)
- \( 3d_{yz}^1 \)
- \( 3d_{zx}^1 \)

This indicates that each of the three d orbitals (t2g) has one electron.

### Conclusion:
The correct distribution of 3d electrons in the chromium of the complex `[Cr(H2O)6]Cl3` is:
\[ 3d_{xy}^1, 3d_{yz}^1, 3d_{zx}^1 \]