Choose the correct statement(s) among the following:

Options

A. `[FeCl_(4)]^(-)` has tetrahedral geometry.
B. `[Co(en)(NH_(3))_(2)Cl_(2)]^(+)` has 2 geometrical isomers.
C. `[FeCl_(4)]^(-)` has higher spin - only magnetic moment than `[Co(en)(CH_(3))_(2)Cl_(2)]^(+)`.
D. The cobalt ion in `[Co(en)(NH_(3))_(2)Cl_(2)]^(+)` has `sp^(3)d^(2)` hybridization.

Explanation

To solve the question, we need to analyze each of the four statements provided and determine which ones are correct. Let's break it down step by step.

### Step 1: Analyze Statement 1
**Statement 1:** FeCl4⁻ has tetrahedral geometry.

1. **Determine the oxidation state of Fe in FeCl4⁻:**
- The charge of chloride (Cl) is -1. Since there are 4 chloride ions, the total negative charge contributed by Cl is -4.
- Let the oxidation state of Fe be x. Therefore, the equation is:
\[ x + 4(-1) = -1 \implies x - 4 = -1 \implies x = +3 \]

2. **Determine the hybridization:**
- Fe in the +3 oxidation state has the electronic configuration of [Ar] 3d⁵.
- The four chloride ions will act as ligands. Since Cl is a weak field ligand, it does not cause pairing of the d-electrons.
- The hybridization can be determined as follows:
- One s orbital and three p orbitals are used for hybridization, resulting in sp³ hybridization.
- sp³ hybridization corresponds to a tetrahedral geometry.

**Conclusion for Statement 1:** This statement is correct.

### Step 2: Analyze Statement 2
**Statement 2:** [Co(en)2Cl2]⁺ shows geometrical isomerism.

1. **Identify the coordination number and geometry:**
- Cobalt (Co) in this complex is in the +3 oxidation state and has a coordination number of 6.
- The geometry for coordination number 6 is octahedral.

2. **Geometrical isomerism:**
- In an octahedral complex, geometrical isomerism can occur when there are different arrangements of ligands.
- The complex can have cis and trans isomers based on the arrangement of the two ethylenediamine (en) ligands and the two chloride (Cl) ligands.
- The possible arrangements are:
- **Cis isomer:** Both Cl ligands adjacent to each other.
- **Trans isomer:** Cl ligands opposite each other.

**Conclusion for Statement 2:** This statement is correct, as geometrical isomerism is possible.

### Step 3: Analyze Statement 3
**Statement 3:** FeCl4⁻ has a higher spin magnetic moment than [Co(en)2Cl2]⁺.

1. **Magnetic moment of FeCl4⁻:**
- As established, FeCl4⁻ has a tetrahedral geometry with sp³ hybridization.
- In tetrahedral complexes, the d-orbitals are split in such a way that the energy of the higher orbitals is lower than that of the lower orbitals, leading to unpaired electrons.
- Fe in +3 state has 5 unpaired electrons (3d⁵).

2. **Magnetic moment of [Co(en)2Cl2]⁺:**
- Co in this complex is in the +3 oxidation state (3d⁶).
- Since ethylenediamine (en) is a strong field ligand, it causes pairing of electrons in the d-orbitals.
- Therefore, [Co(en)2Cl2]⁺ has no unpaired electrons.

**Conclusion for Statement 3:** This statement is correct, as FeCl4⁻ has more unpaired electrons than [Co(en)2Cl2]⁺.

### Step 4: Analyze Statement 4
**Statement 4:** The hybridization of [Co(en)2Cl2]⁺ is dsp³.

1. **Determine the hybridization:**
- As established, [Co(en)2Cl2]⁺ has an octahedral geometry.
- The hybridization for octahedral complexes is typically d²sp³, not dsp³.

**Conclusion for Statement 4:** This statement is incorrect.

### Final Answer
The correct statements are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect

Thus, the correct statements are A, B, and C.