The correct option(s) regarding the complex `[Co(en)(NH_(3))_(3)(H_(2)O)]_(3)+ en = H_(2)NCH_(2)CH_(2)NH_(2)` is (are)

Options

A. It has two geometrical isomers
B. It will have three geometrical isomers if bidentate 'en' is replaced by two cyanide ligands
C. It is paramagnetic
D. It absorbs light at longer wavelength as compared to `[Co(en)NH_(3))_(4)]^(3+)`

Answer

To solve the question regarding the complex \([Co(en)(NH_3)_3(H_2O)]^{3+}\) where \(en = H_2NCH_2CH_2NH_2\) (ethylene diamine), we will analyze the properties and characteristics of the complex step by step.

### Step 1: Identify the Ligands and Their Properties
The complex consists of:
- \(Co^{3+}\) as the central metal ion.
- Ethylene diamine (en), which is a bidentate ligand.
- Three ammonia (NH3) ligands, which are monodentate.
- One water (H2O) ligand, which is also monodentate.

**Hint:** Remember that bidentate ligands can attach to the metal at two points, while monodentate ligands attach at one point.

### Step 2: Determine the Oxidation State of Cobalt
The overall charge of the complex is +3. Since the ligands (en, NH3, and H2O) are neutral, the oxidation state of cobalt can be determined as follows:
\[ \text{Oxidation state of } Co + 0 + 0 + 0 = +3 \]
Thus, the oxidation state of cobalt in this complex is +3.

**Hint:** The charge of the complex can help you find the oxidation state of the central metal ion.

### Step 3: Analyze the Geometry of the Complex
Cobalt(III) complexes with a coordination number of 6 typically exhibit octahedral geometry. In this case, the arrangement of the ligands can lead to different geometrical isomers.

**Hint:** Visualize the arrangement of ligands around the central metal to identify possible isomers.

### Step 4: Identify Possible Geometrical Isomers
The complex can have two types of geometrical isomers:
1. **Facial (fac)**: where two of the same type of ligands are adjacent to each other.
2. **Meridional (mer)**: where the same type of ligands are arranged in a plane.

In this case, the two isomers arise from the arrangement of the three NH3 ligands and the H2O ligand relative to the bidentate en ligand.

**Hint:** Sketching the structure can help visualize the facial and meridional arrangements.

### Step 5: Determine Magnetic Properties
Cobalt in the +3 oxidation state has the electron configuration of \(Ar 3d^6\). Since both en and NH3 are strong field ligands, they will cause pairing of electrons in the \(3d\) orbitals, resulting in a diamagnetic complex (no unpaired electrons).

**Hint:** The type of ligands (strong or weak field) influences whether the complex is paramagnetic or diamagnetic.

### Step 6: Compare Light Absorption with Other Complexes
When comparing the complex \([Co(en)(NH_3)_3(H_2O)]^{3+}\) with \([Co(en)(NH_3)_4]^{3+}\), the addition of a strong field ligand (NH3) instead of a weak field ligand (H2O) increases the crystal field splitting energy (\(\Delta\)). Therefore, the complex in the question will absorb light at a longer wavelength than \([Co(en)(NH_3)_4]^{3+}\).

**Hint:** The nature of the ligands affects the energy levels of the d-orbitals, which in turn affects light absorption.

### Conclusion
Based on the analysis:
- The complex has two geometrical isomers (fac and mer).
- It is diamagnetic due to all electrons being paired.
- It absorbs light at a longer wavelength compared to \([Co(en)(NH_3)_4]^{3+}\).

Thus, the correct options regarding the complex are:
1. It has two geometrical isomers.
2. It is diamagnetic.
3. It absorbs light at a longer wavelength compared to \([Co(en)(NH_3)_4]^{3+}\).