The radius `La^(3+)` (Z= 57) is 106 pm . Which one of the following given values will be closet to the radius of `Lu^(3+)` (Z = 71) ?

Options

A. 160 Pm
B. 140 pm
C. 106 pm
D. 85 pm

Explanation

To determine the radius of `Lu^(3+)` (Z = 71) based on the given radius of `La^(3+)` (Z = 57), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Lanthanide Contraction**:
- The lanthanide contraction refers to the gradual decrease in the size of the lanthanide ions as the atomic number increases from La to Lu. This occurs due to the poor shielding effect of the f-electrons, which leads to a stronger effective nuclear charge experienced by the outer electrons.

2. **Given Data**:
- The radius of `La^(3+)` (Z = 57) is 106 pm.

3. **Identify the Trend**:
- As we move from La to Lu, the ionic radius decreases. The radius of `La^(3+)` is 106 pm, and we need to find the radius of `Lu^(3+)`.

4. **Estimate the Radius of `Lu^(3+)`**:
- Based on the trend observed in the lanthanide series, the radius of `Lu^(3+)` is expected to be smaller than that of `La^(3+)`.
- The radius of `Lu^(3+)` is typically found to be around 85 pm based on the trend of decreasing ionic radii in the series.

5. **Select the Closest Value**:
- From the options provided: 160 pm, 140 pm, 106 pm, and 85 pm, the closest value to the expected radius of `Lu^(3+)` is 85 pm.

### Final Answer:
The radius of `Lu^(3+)` is closest to **85 pm**.

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