The type of hybridisation and magnetic property og the complex `[MnCl_(6)]^(3-)`, respectively, are :

Options

A. `sp^(3) d^(2)` and diamagnetic
B. `d^(2) sp^(3)` and diamagnetic
C. `d^(2)sp^(3)` and paramagnetic
D. `sp^(3)d^(2)` and paramagnetic

Answer

To determine the type of hybridization and magnetic property of the complex \([MnCl_6]^{3-}\), we can follow these steps:

### Step 1: Determine the oxidation state of manganese (Mn)
- The complex \([MnCl_6]^{3-}\) has a charge of -3. Each chloride ion (Cl) has a charge of -1.
- Let the oxidation state of manganese be \(x\).
- The equation can be set up as:
\[ x + 6(-1) = -3 \]
\[ x - 6 = -3 \implies x = +3 \]
- Thus, the oxidation state of manganese in this complex is +3.

### Step 2: Write the electron configuration of manganese
- The atomic number of manganese (Mn) is 25. Its ground state electron configuration is:
\[ [Ar] 3d^5 4s^2 \]
- For \(Mn^{3+}\), we remove 3 electrons (2 from 4s and 1 from 3d):
\[ [Ar] 3d^4 \]

### Step 3: Determine the geometry of the complex
- The complex \([MnCl_6]^{3-}\) is an octahedral complex because it has six ligands (Cl).
- However, due to the presence of a transition metal with unpaired electrons, it may exhibit distortion (John-Teller distortion).

### Step 4: Identify the hybridization
- In an octahedral complex, the hybridization is typically \(d^2sp^3\) or \(sp^3d^2\).
- For \(Mn^{3+}\) with a \(3d^4\) configuration, the hybridization will be \(d^2sp^3\) because the \(d\) orbitals are involved in bonding.

### Step 5: Determine the magnetic property
- The \(3d^4\) configuration means there are 4 electrons in the \(d\) orbitals.
- In an octahedral field, the \(d\) orbitals split into two sets: \(t_{2g}\) and \(e_g\).
- The \(t_{2g}\) orbitals can hold 6 electrons, while the \(e_g\) orbitals can hold 4 electrons.
- With 4 electrons in \(3d^4\), we can fill the \(t_{2g}\) orbitals first (3 electrons) and then one electron in the \(e_g\) orbital (1 electron).
- This results in unpaired electrons, indicating that the complex is **paramagnetic**.

### Conclusion
- The type of hybridization for \([MnCl_6]^{3-}\) is \(d^2sp^3\).
- The magnetic property of the complex is paramagnetic.

### Final Answer
- The type of hybridization and magnetic property of the complex \([MnCl_6]^{3-}\) are: **\(d^2sp^3\) hybridization and paramagnetic**.