Which of the following is//are characteristic of a tetrahedral complex ?

Options

A. `a.d_(x)2-_(y)2` and `d_(z)2` orbitals are low energy orbitals
B. b.Most tetrahedral complexes are high spin
C. c.Crystal field splitting is found double in octahedral complexes .
D. d.Splitting pattern in tetrahedral complex is just opposite of that in octahedral complexes.

Answer

To determine the characteristics of tetrahedral complexes, we need to analyze the properties and behavior of these complexes based on their electronic structure and crystal field theory. Here’s a step-by-step solution to the question:

### Step 1: Understand the Hybridization
Tetrahedral complexes exhibit **sp³ hybridization**. This means that one s orbital and three p orbitals mix to form four equivalent sp³ hybrid orbitals that are oriented towards the corners of a tetrahedron.

**Hint**: Remember that tetrahedral complexes are formed when a central metal atom is surrounded by four ligands.

### Step 2: Analyze d-Orbital Splitting
In tetrahedral complexes, the d-orbitals split into two sets due to the presence of ligands. The splitting pattern results in:
- **T2g** (higher energy orbitals)
- **Eg** (lower energy orbitals)

In tetrahedral complexes, the energy of the T2g orbitals is higher than that of the Eg orbitals.

**Hint**: Visualize the d-orbital splitting diagram for tetrahedral complexes to understand which orbitals are higher and lower in energy.

### Step 3: Determine Spin State
Most tetrahedral complexes are **high spin** complexes. This is because the energy difference between the T2g and Eg orbitals is relatively small, allowing electrons to occupy higher energy orbitals rather than pairing up in the lower energy orbitals.

**Hint**: High spin complexes have unpaired electrons, which can be identified by considering the arrangement of electrons in the d-orbitals.

### Step 4: Compare Crystal Field Splitting
The crystal field splitting energy (Δ) in tetrahedral complexes is less than that in octahedral complexes. Specifically, the relationship can be expressed as:
\[ \Delta_t = \frac{4}{9} \Delta_o \]
where Δ_t is the splitting in tetrahedral complexes and Δ_o is the splitting in octahedral complexes.

**Hint**: Keep in mind that the ratio of the splitting energies helps in distinguishing between tetrahedral and octahedral complexes.

### Step 5: Identify the Splitting Pattern
The splitting pattern in tetrahedral complexes is opposite to that in octahedral complexes. In octahedral complexes, the Eg orbitals are higher in energy than the T2g orbitals, whereas in tetrahedral complexes, the T2g orbitals are higher in energy than the Eg orbitals.

**Hint**: Draw the energy level diagrams for both tetrahedral and octahedral complexes to visualize the differences in splitting patterns.

### Conclusion
Based on the analysis, the characteristics of tetrahedral complexes include:
1. **dx²-y² and dz² are low energy orbitals** (correct).
2. **Most tetrahedral complexes have a high spin** (correct).
3. **Crystal field splitting found double in octahedral** (incorrect).
4. **Splitting pattern in tetrahedral complexes is opposite to that of octahedral complexes** (correct).

Thus, the correct options are 1, 2, and 4.

### Final Answer
The characteristics of tetrahedral complexes are:
- Option 1: dx²-y² and dz² are low energy orbitals (Correct).
- Option 2: Most tetrahedral complexes have a high spin (Correct).
- Option 3: Crystal field splitting found double in octahedral (Incorrect).
- Option 4: Splitting pattern in tetrahedral complexes is opposite to that of octahedral complexes (Correct).