For the complex `[Ma_2B_2]` if M is `sp^3` or `dsp^2` hybridised respectively then total number of optical isomers are respectively:

Options

A. 1,1
B. 2,1
C. 0,0
D. 1,2

Answer

To determine the total number of optical isomers for the complex \([Ma_2B_2]\) when \(M\) is \(sp^3\) or \(dsp^2\) hybridized, we need to analyze the geometry and symmetry of the complexes formed in each case.

### Step 1: Analyze the \(sp^3\) Hybridization
1. **Identify the Geometry**: For \(sp^3\) hybridization, the geometry of the complex \([Ma_2B_2]\) is tetrahedral.
2. **Determine Optical Isomerism**: In a tetrahedral complex, optical isomerism can occur if there is no plane of symmetry and if all four ligands are different. However, in this case, since we have two identical ligands \(A\) and two identical ligands \(B\), there will be a plane of symmetry present.
3. **Conclusion for \(sp^3\)**: Because of the symmetry, the tetrahedral complex does not exhibit optical isomerism. Therefore, the number of optical isomers for the \(sp^3\) hybridized complex is **0**.

### Step 2: Analyze the \(dsp^2\) Hybridization
1. **Identify the Geometry**: For \(dsp^2\) hybridization, the geometry of the complex \([Ma_2B_2]\) is square planar.
2. **Determine Optical Isomerism**: In square planar complexes, optical isomerism can occur if the arrangement of ligands does not allow for a plane of symmetry. In the case of \([Ma_2B_2]\), we can have two arrangements: cis and trans.
- **Cis Configuration**: In the cis configuration, the two \(A\) ligands are adjacent, and the two \(B\) ligands are adjacent. This arrangement has a plane of symmetry.
- **Trans Configuration**: In the trans configuration, the \(A\) ligands are opposite each other, and the \(B\) ligands are also opposite each other. This arrangement also has a plane of symmetry.
3. **Conclusion for \(dsp^2\)**: Since both configurations (cis and trans) have a plane of symmetry, the square planar complex does not exhibit optical isomerism. Therefore, the number of optical isomers for the \(dsp^2\) hybridized complex is also **0**.

### Final Answer
Thus, the total number of optical isomers for the complex \([Ma_2B_2]\) is:
- For \(sp^3\) hybridized: **0**
- For \(dsp^2\) hybridized: **0**

### Summary
The final answer is:
- Total number of optical isomers for \(sp^3\): 0
- Total number of optical isomers for \(dsp^2\): 0