A: `La(OH)_(3)`, is less basic than `Lu(OH)_(3)`,
R: Basic character of hydroxides of lanthanoids increase on moving from `La^(+3)`to `Lu^(+3)`

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To analyze the given statements regarding the basicity of lanthanum hydroxide (La(OH)₃) and lutetium hydroxide (Lu(OH)₃), we can break down the reasoning step by step.

### Step 1: Understanding the Assertion
The assertion states that La(OH)₃ is less basic than Lu(OH)₃. To evaluate this, we need to consider the basicity of hydroxides in the lanthanide series.

### Step 2: Basicity of Lanthanide Hydroxides
The basicity of hydroxides generally increases with the ionic size of the metal cation. In the case of lanthanides, as we move from La³⁺ to Lu³⁺, the size of the cation decreases due to lanthanide contraction. This contraction occurs because of the poor shielding effect of the 4f electrons.

### Step 3: Effect of Cation Size on Basicity
As the cation size decreases:
- The covalent character of the hydroxides increases.
- The acidic character of the hydroxides increases as well.

This means that smaller cations (like Lu³⁺) will form more covalent and, therefore, more acidic hydroxides compared to larger cations (like La³⁺). Hence, La(OH)₃, which has a larger cation, will be more basic than Lu(OH)₃.

### Step 4: Evaluating the Reason
The reason states that the basic character of hydroxides of lanthanides increases from La³⁺ to Lu³⁺. However, based on our analysis, this statement is incorrect. The basic character actually decreases as we move from La³⁺ to Lu³⁺ due to the reasons outlined above.

### Conclusion
Both the assertion and the reason are incorrect:
- Assertion: La(OH)₃ is less basic than Lu(OH)₃ (False)
- Reason: Basic character of hydroxides of lanthanides increases from La³⁺ to Lu³⁺ (False)

Thus, the correct answer is that both the assertion and the reason are false.

### Final Answer
Both the assertion and the reason are false.

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