Which of the following trivalent ion has the largest atomic radii in the lanthanide series

Options

A. La
B. Ce
C. Pm
D. Lu

Explanation

To determine which of the following trivalent ions has the largest atomic radii in the lanthanide series, we will analyze the options provided: Lanthanum (La³⁺), Cerium (Ce³⁺), Promethium (Pm³⁺), and Lutetium (Lu³⁺).

### Step-by-Step Solution:

1. **Identify the Elements**: The elements in question are:
- Lanthanum (La)
- Cerium (Ce)
- Promethium (Pm)
- Lutetium (Lu)

2. **Understand the Trend in the Lanthanide Series**: The lanthanide series consists of elements with atomic numbers from 57 (Lanthanum) to 71 (Lutetium). As we move from Lanthanum to Lutetium, the atomic number increases, and the size of the ions generally decreases.

3. **Reason for Decrease in Size**: The decrease in ionic radii across the lanthanide series can be attributed to the increasing nuclear charge. As the atomic number increases, the positive charge in the nucleus increases, pulling the electrons closer to the nucleus and resulting in a smaller ionic radius.

4. **Identify the Largest Ion**: Among the trivalent ions (La³⁺, Ce³⁺, Pm³⁺, Lu³⁺):
- La³⁺ has the largest ionic radius because it is the first element in the series.
- As we progress to Ce³⁺, Pm³⁺, and Lu³⁺, the ionic radii decrease due to the reasons mentioned above.

5. **Conclusion**: Therefore, Lanthanum (La³⁺) has the largest atomic radii among the given trivalent ions in the lanthanide series.

### Final Answer:
The trivalent ion with the largest atomic radii in the lanthanide series is **Lanthanum (La³⁺)**.