Which is correct

Options

A. `Ce(OH)_(3)` is weaker base than `Lu(OH)_(3)` .
B. `E_(Mn^(3+)//Mn^(2+))^(@)` is more positive than `Fe^(3+)//Fe^(2+)`
C. `Ti gt Zr gt Hf ` (Group 4 atomic radii )
D. Lanthanides are not separated by ion exchange method

Answer

To solve the question, we need to evaluate the correctness of the statements mentioned in the video transcript regarding cerium oxide, manganese, titanium, and lanthanides.

### Step-by-Step Solution:

1. **Evaluate the first statement:**
- **Statement:** Cerium oxide is weaker than deuterium hydroxide.
- **Analysis:** The basic character of hydroxides in the lanthanide series decreases due to lanthanide contraction. As we move from La³⁺ to Lu³⁺, the size decreases, leading to an increase in covalent character and a decrease in basic strength. Therefore, Ce(OH)₃ is stronger than Lu(OH)₃, making this statement false.

2. **Evaluate the second statement:**
- **Statement:** E° (Mn³⁺ / Mn²⁺) is more positive than E° (Fe³⁺ / Fe²⁺).
- **Analysis:** The electronic configuration of Mn³⁺ is [Ar] 4s⁰ 3d⁴, and when it gains an electron, it becomes [Ar] 4s⁰ 3d⁵, which is a stable half-filled configuration. In contrast, Fe³⁺ has a configuration of [Ar] 4s⁰ 3d⁵, and gaining an electron to become Fe²⁺ (which is [Ar] 4s² 3d⁶) is less stable. Thus, E° (Mn³⁺ / Mn²⁺) is indeed more positive than E° (Fe³⁺ / Fe²⁺), making this statement true.

3. **Evaluate the third statement:**
- **Statement:** The order of group 4 atomic radii is Ti > Zr > Hf.
- **Analysis:** As we move down a group, atomic radii generally increase. However, Zr and Hf have similar radii due to poor shielding by the f-orbitals. Therefore, the correct order should be Ti > Zr ≈ Hf, making this statement false.

4. **Evaluate the fourth statement:**
- **Statement:** Lanthanides are not separated by ion exchange method.
- **Analysis:** This statement is incorrect. Lanthanides can be separated by ion exchange methods based on solubility differences in their nitrates, oxalates, and fluorides. The ion exchange method is a modern technique for separating lanthanides, so this statement is also false.

### Conclusion:
Based on the evaluations:
- The correct statement is **Statement B**: E° (Mn³⁺ / Mn²⁺) is more positive than E° (Fe³⁺ / Fe²⁺).