Consider the following statements
(I) `Zr^(4+)` and `Hf^(4+)` have almost same ionic radii
(II) Lanthanoids liberate `H_2` when treated with dilute acids.
(III) The ionic radii of trivalent lanthanoids steadily increase with increase in atomic number.
The correct statement(s) is/ are

Options

A. I ,II
B. I , III
C. Only II
D. I, II, III

Answer

To solve the question, we need to analyze each of the three statements provided regarding Zr^(4+), Hf^(4+), lanthanoids, and their properties.

### Step 1: Analyze Statement I
**Statement I:** Zr^(4+) and Hf^(4+) have almost the same ionic radii.

- **Explanation:** Zirconium (Zr) and Hafnium (Hf) are both in Group 4 of the periodic table. Zr is in the 4th period, while Hf is in the 5th period. Due to the lanthanoid contraction, the ionic radii of Zr^(4+) and Hf^(4+) are indeed very similar. Therefore, this statement is **correct**.

### Step 2: Analyze Statement II
**Statement II:** Lanthanoids liberate H2 when treated with dilute acids.

- **Explanation:** Lanthanoids (the 14 elements from Cerium to Lutetium) react with dilute acids to liberate hydrogen gas (H2). This is a well-known property of these metals. Therefore, this statement is also **correct**.

### Step 3: Analyze Statement III
**Statement III:** The ionic radii of trivalent lanthanoids steadily increase with an increase in atomic number.

- **Explanation:** This statement is **incorrect**. The ionic radii of trivalent lanthanoids actually decrease with an increase in atomic number due to the lanthanoid contraction. As the atomic number increases, electrons are added to the 4f subshell, which has poor shielding effects, leading to a stronger effective nuclear charge and thus a decrease in ionic size.

### Conclusion
Based on the analysis:
- Statement I is correct.
- Statement II is correct.
- Statement III is incorrect.

Thus, the correct statements are I and II.

### Final Answer
The correct statements are I and II.