The pair of lanthanides with the highest third ionization energy is

Options

A. `Lu` and `Yb`
B. `Eu` and `Gd`
C. `Eu` and `Yb`
D. `Dy` and `Yb`

Explanation

To determine the pair of lanthanides with the highest third ionization energy, we will analyze the electronic configurations of the relevant lanthanides and their ionization energies.

### Step-by-Step Solution:

1. **Identify the Lanthanides**: The lanthanides are a series of 15 elements from cerium (Ce) to lutetium (Lu) in the periodic table. We will focus on the pairs of lanthanides that are commonly known for their ionization energies.

2. **Write the Electronic Configurations**: We need to write down the electronic configurations for the lanthanides in question. For the purpose of this question, let’s consider the following lanthanides:
- Lutetium (Lu): [Xe] 4f¹⁴ 5d¹ 6s²
- Ytterbium (Yb): [Xe] 4f¹⁴ 6s²
- Europium (Eu): [Xe] 4f⁷ 6s²
- Gadolinium (Gd): [Xe] 4f⁷ 5d¹ 6s²
- Dysprosium (Dy): [Xe] 4f¹⁰ 6s²

3. **Understand Ionization Energy**: The third ionization energy refers to the energy required to remove the third electron from an atom. Generally, the removal of electrons from a fully filled or half-filled subshell requires more energy due to increased stability.

4. **Analyze Stability of Configurations**:
- Ytterbium (Yb) has a fully filled 4f subshell, making it stable.
- Europium (Eu) has a half-filled 4f subshell (4f⁷), which also contributes to stability.
- Lutetium (Lu) has a filled 4f subshell and a partially filled 5d subshell, which can influence its ionization energy.

5. **Determine the Highest Third Ionization Energy**:
- Ytterbium (Yb) is likely to have the highest third ionization energy due to its fully filled 4f subshell.
- Europium (Eu) would have a lower third ionization energy than Yb because it has a half-filled subshell.
- Lutetium (Lu) would also have a high ionization energy but not as high as Yb.

6. **Conclusion**: The pair of lanthanides with the highest third ionization energy is **Ytterbium (Yb) and Lutetium (Lu)**.