Which element among the lanthanides has the smallest atomic radius

Options

A. Cerium
B. Lutetium
C. Europium
D. Gadolinium

Answer

To determine which element among the lanthanides has the smallest atomic radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lanthanide Series**: The lanthanides consist of 15 elements from lanthanum (La) to lutetium (Lu). They are typically listed in order of increasing atomic number.

2. **Identify the Elements**: The elements mentioned in the question are:
- Cerium (Ce)
- Europium (Eu)
- Gadolinium (Gd)
- Lutetium (Lu)

3. **Atomic Radius Trend in Lanthanides**: As we move from left to right across the lanthanide series, the atomic radius generally decreases. This is due to the increase in the number of protons in the nucleus, which leads to a greater positive charge that pulls the electrons closer to the nucleus.

4. **Lanthanide Contraction**: The phenomenon known as lanthanide contraction occurs due to the poor shielding effect of the 4f electrons. As we progress through the series, the effective nuclear charge increases, resulting in a decrease in atomic size.

5. **Compare the Atomic Radii**:
- Cerium (Ce) has a larger atomic radius compared to Lutetium (Lu).
- Europium (Eu) and Gadolinium (Gd) also have larger atomic radii than Lutetium (Lu).
- Lutetium (Lu), being the last element in the series, has the smallest atomic radius due to the maximum number of protons and the effects of lanthanide contraction.

6. **Conclusion**: Among the given options, Lutetium (Lu) has the smallest atomic radius.

### Final Answer:
Lutetium (Lu) has the smallest atomic radius among the lanthanides listed.

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