The 'f' orbitals are half and completely filled, respectively in lanthanide ions
[Given : Atomic no . Eu, 63, Sm, 62 , Tm, 69 , Tb, 65 , Yb, 70 , Dy, 66]`

Options

A. `Eu^(2+) and Tm^(2+)`
B. `Sm^(2+) and Tm^(3+)`
C. `Tb^(4-) and Yb^(2+)`
D. `Dy^(3+) and Yb^(3+)`

Explanation

To determine which lanthanide ions have half-filled and completely filled 'f' orbitals, we need to analyze the electron configurations of the given lanthanide ions based on their atomic numbers.

### Step-by-Step Solution:

1. **Identify the Electron Configuration of Lanthanides:**
The lanthanides are elements with atomic numbers from 57 (Lanthanum) to 71 (Lutetium). The 'f' orbitals start filling from Lanthanum (La) which has the electron configuration of [Xe] 6s² 5d¹. The 'f' orbitals begin to fill from Cerium (Ce, atomic number 58) onwards.

2. **Determine the Electron Configuration for Each Ion:**
- **Europium (Eu, atomic number 63):**
- Neutral Eu: [Xe] 6s² 4f⁷
- Eu²⁺: [Xe] 6s² 4f⁷ → 4f⁷ (removing 2 electrons from 6s)
- **Samarium (Sm, atomic number 62):**
- Neutral Sm: [Xe] 6s² 4f⁶
- Sm²⁺: [Xe] 6s² 4f⁶ → 4f⁶
- **Thulium (Tm, atomic number 69):**
- Neutral Tm: [Xe] 6s² 4f¹³
- Tm²⁺: [Xe] 6s² 4f¹³ → 4f¹³
- **Terbium (Tb, atomic number 65):**
- Neutral Tb: [Xe] 6s² 4f⁷
- Tb³⁺: [Xe] 6s² 4f⁷ → 4f⁷
- **Ytterbium (Yb, atomic number 70):**
- Neutral Yb: [Xe] 6s² 4f¹⁴
- Yb²⁺: [Xe] 6s² 4f¹⁴ → 4f¹⁴
- **Dysprosium (Dy, atomic number 66):**
- Neutral Dy: [Xe] 6s² 4f⁹
- Dy³⁺: [Xe] 6s² 4f⁹ → 4f⁹

3. **Identify Half-Filled and Fully Filled States:**
- The 'f' subshell can hold a maximum of 14 electrons.
- Half-filled means having 7 electrons in the 'f' subshell (4f⁷).
- Fully filled means having 14 electrons in the 'f' subshell (4f¹⁴).

4. **List the Ions with Their Configurations:**
- **Eu²⁺:** 4f⁷ (half-filled)
- **Tm²⁺:** 4f¹³ (not half or fully filled)
- **Sm²⁺:** 4f⁶ (not half or fully filled)
- **Tb³⁺:** 4f⁷ (half-filled)
- **Yb²⁺:** 4f¹⁴ (fully filled)
- **Dy³⁺:** 4f⁹ (not half or fully filled)

5. **Conclusion:**
The ions with half-filled and completely filled 'f' orbitals are:
- Half-filled: Eu²⁺ (4f⁷), Tb³⁺ (4f⁷)
- Fully filled: Yb²⁺ (4f¹⁴)

### Final Answer:
- Half-filled: Eu²⁺ and Tb³⁺
- Fully filled: Yb²⁺