`[Fe(H_2O)_6 NO]` and `[Cr(NH_3)_6](NO_2)_3` both are paramagnetic species with 'spin' only magnetic moment of 3.93 B.M. The hybridisation of central metal ions in these species respectively are :

Options

A. Both `sp^3d^2`
B. Both `d^2sp^3`
C. `sop^3d^2 and d^2sp^3`
D. `d^2sp^3 and sp^3d^2`

Explanation

To determine the hybridization of the central metal ions in the complexes `[Fe(H_2O)_6 NO]` and `[Cr(NH_3)_6](NO_2)_3`, we will analyze each complex step by step.

### Step 1: Analyze the first complex `[Fe(H_2O)_6 NO]`

1. **Identify the oxidation state of Iron (Fe)**:
- In the complex, the overall charge is neutral. The water (H2O) and NO ligands are neutral, so the oxidation state of Fe must be +2.

2. **Determine the electronic configuration of Fe in +2 state**:
- The ground state electronic configuration of Fe (atomic number 26) is:
\[ [Ar] 3d^6 4s^2 \]
- After losing 2 electrons (from the 4s orbital), the configuration becomes:
\[ [Ar] 3d^6 \]

3. **Count the number of unpaired electrons**:
- The 3d subshell has 6 electrons. Since H2O is a weak field ligand, it does not cause pairing of electrons. Therefore, the configuration in the 3d subshell can be represented as:
\[ ↑↓ ↑ ↑ ↑ ↑ \]
- There are 4 unpaired electrons.

4. **Determine the hybridization**:
- Since there are 6 ligands (H2O), the hybridization will be:
\[ sp^3d^2 \]

### Step 2: Analyze the second complex `[Cr(NH_3)_6](NO_2)_3`

1. **Identify the oxidation state of Chromium (Cr)**:
- The complex has a neutral charge overall. The ammonia (NH3) ligands are neutral, and the NO2 ligands have a -1 charge. Therefore, the oxidation state of Cr must be +3.

2. **Determine the electronic configuration of Cr in +3 state**:
- The ground state electronic configuration of Cr (atomic number 24) is:
\[ [Ar] 3d^5 4s^1 \]
- After losing 3 electrons (2 from 4s and 1 from 3d), the configuration becomes:
\[ [Ar] 3d^3 \]

3. **Count the number of unpaired electrons**:
- The 3d subshell has 3 electrons. Since NH3 is also a weak field ligand, it does not cause pairing of electrons. Therefore, the configuration in the 3d subshell can be represented as:
\[ ↑ ↑ ↑ \]
- There are 3 unpaired electrons.

4. **Determine the hybridization**:
- Since there are 6 ligands (NH3), the hybridization will be:
\[ d^2sp^3 \]

### Final Answer:
- The hybridization of the central metal ions in the complexes are:
- For `[Fe(H_2O)_6 NO]`: **sp³d²**
- For `[Cr(NH_3)_6](NO_2)_3`: **d²sp³**