Which of the following elements have half-filled f-orbitals in their ground state?
(Given : atomic number Sm - 62, Eu=63, Tb=65, Gd = 64,Pm=61)
`A. Sm`,` B. Eu `,` C.Tb `,` D.Gd `,` E.Pm `
Choose the correct answer from the options given below :

Options

A. `A` and `B` only
B. `C` and `D` only
C. `B` and `D` only
D. `A` and `E` only

Answer

To determine which of the given elements have half-filled f-orbitals in their ground state, we need to analyze the electronic configurations of each element based on their atomic numbers.

### Step-by-Step Solution:

1. **Identify the Atomic Numbers and Elements**:
- Samarium (Sm) - Atomic number 62
- Europium (Eu) - Atomic number 63
- Terbium (Tb) - Atomic number 65
- Gadolinium (Gd) - Atomic number 64
- Promethium (Pm) - Atomic number 61

2. **Write the Electronic Configurations**:
- **Samarium (Sm, Z=62)**:
- Electronic configuration: [Xe] 4f^6 6s^2
- **Europium (Eu, Z=63)**:
- Electronic configuration: [Xe] 4f^7 6s^2
- **Terbium (Tb, Z=65)**:
- Electronic configuration: [Xe] 4f^9 6s^2
- **Gadolinium (Gd, Z=64)**:
- Electronic configuration: [Xe] 4f^7 5d^1 6s^2
- **Promethium (Pm, Z=61)**:
- Electronic configuration: [Xe] 4f^5 6s^2

3. **Determine Half-filled f-orbitals**:
- A half-filled f-orbital configuration for f-block elements occurs when there are 5 electrons in the f-orbitals (4f^5).
- For 4f orbitals, the following configurations are relevant:
- Half-filled: 4f^5
- More than half-filled: 4f^6, 4f^7, 4f^8, 4f^9

4. **Analyze Each Element**:
- **Samarium (Sm)**: 4f^6 (not half-filled)
- **Europium (Eu)**: 4f^7 (not half-filled)
- **Terbium (Tb)**: 4f^9 (not half-filled)
- **Gadolinium (Gd)**: 4f^7 5d^1 (not half-filled)
- **Promethium (Pm)**: 4f^5 (half-filled)

5. **Conclusion**:
- The only element with half-filled f-orbitals in its ground state is **Promethium (Pm)**.

### Answer:
The correct answer is **E. Pm**.