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 1: Identify the Lanthanide Series
The lanthanide series consists of 15 elements, starting from Cerium (Ce, atomic number 58) to Lutetium (Lu, atomic number 71). The elements in this series are:
- Cerium (Ce, 58)
- Praseodymium (Pr, 59)
- Neodymium (Nd, 60)
- Promethium (Pm, 61)
- Samarium (Sm, 62)
- Europium (Eu, 63)
- Gadolinium (Gd, 64)
- Terbium (Tb, 65)
- Dysprosium (Dy, 66)
- Holmium (Ho, 67)
- Erbium (Er, 68)
- Thulium (Tm, 69)
- Ytterbium (Yb, 70)
- Lutetium (Lu, 71)

### Step 2: Understand Atomic Radius Trends
In the lanthanide series, as we move from left to right, the atomic number increases while the number of electron shells remains the same. This results in an increase in the positive charge of the nucleus, which leads to a stronger attraction between the nucleus and the electrons. Consequently, the atomic radius decreases.

### Step 3: Analyze the Options
The options provided are:
1. Cerium (Ce)
2. Lutetium (Lu)
3. Europium (Eu)
4. Gadolinium (Gd)

### Step 4: Determine the Smallest Atomic Radius
Among the lanthanides, Lutetium (Lu) has the highest atomic number (71) and therefore the smallest atomic radius due to the increased nuclear charge and the corresponding decrease in atomic size.

### Conclusion
Thus, the element among the lanthanides that has the smallest atomic radius is **Lutetium (Lu)**.

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