Which of the following elements has half filled f-orbitals ?

Options

A. only Eu
B. only Eu and Yb
C. Only Gd
D. only Eu and Gd

Answer

To determine which element has half-filled f-orbitals, we need to analyze the electronic configurations of the elements provided. Let's go through the steps systematically.

### Step 1: Identify the Elements
Let's consider the elements mentioned in the question: Europium (Eu), Gadolinium (Gd), and Ytterbium (Yb).

### Step 2: Write the Electronic Configurations
1. **Europium (Eu)**:
- Atomic number: 63
- Electronic configuration: [Xe] 4f^7 6s^2

2. **Gadolinium (Gd)**:
- Atomic number: 64
- Electronic configuration: [Xe] 4f^7 5d^1 6s^2

3. **Ytterbium (Yb)**:
- Atomic number: 70
- Electronic configuration: [Xe] 4f^{14} 6s^2

### Step 3: Determine the Filling of f-Orbitals
- The f-orbitals can hold a maximum of 14 electrons (2 electrons per orbital, with 7 orbitals).
- A half-filled f-orbital configuration means that there are 7 electrons in the f-orbitals.

### Step 4: Analyze Each Element
- **Europium (Eu)**: Has 7 electrons in the 4f subshell (4f^7). This is half-filled.
- **Gadolinium (Gd)**: Also has 7 electrons in the 4f subshell (4f^7). This is half-filled.
- **Ytterbium (Yb)**: Has 14 electrons in the 4f subshell (4f^{14}). This is not half-filled.

### Step 5: Conclusion
From the analysis, both Europium (Eu) and Gadolinium (Gd) have half-filled f-orbitals. Therefore, the correct answer is that both Europium and Gadolinium have half-filled f-orbitals.

### Final Answer
**Europium (Eu) and Gadolinium (Gd) have half-filled f-orbitals.**

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