The electronic configuration of tetravalent terbium and divalent ytterbium are :
(Atomic number : Xe = 54, Tb = 65, Yb = 70)

Options

A. `[Xe]4f^(8) and [Xe]4f^(13)`
B. `[Xe]4f^(7) and [Xe]4f^(14)`
C. `[Xe]4f^(8)6s^(1) and [Xe]4f^(13)6s^(1)`
D. `[Xe]4f^(8) and [Xe]4f^(14)`

Explanation

To find the electronic configurations of tetravalent terbium (Tb) and divalent ytterbium (Yb), we will follow these steps:

### Step 1: Determine the Ground State Electronic Configurations
1. **Identify the atomic numbers**:
- Terbium (Tb) has an atomic number of 65.
- Ytterbium (Yb) has an atomic number of 70.
- The atomic number of Xenon (Xe) is 54.

2. **Write the ground state electronic configuration**:
- The ground state electronic configuration of Tb (atomic number 65) is:
- Start with the configuration of Xe (54):
- Xe: [Xe] = 4f^14 5s^2 5p^6
- Then add the remaining electrons:
- Tb: [Xe] 4f^9 6s^2
- The ground state electronic configuration of Yb (atomic number 70) is:
- Yb: [Xe] 4f^14 6s^2

### Step 2: Determine the Electronic Configuration for Tetravalent Terbium
1. **Understand tetravalent**:
- Tetravalent means that terbium has lost 4 electrons.
- Starting from the ground state configuration of Tb: [Xe] 4f^9 6s^2

2. **Remove 4 electrons**:
- Remove 2 electrons from the 6s subshell and 2 electrons from the 4f subshell:
- Resulting configuration for Tb^4+: [Xe] 4f^7

### Step 3: Determine the Electronic Configuration for Divalent Ytterbium
1. **Understand divalent**:
- Divalent means that ytterbium has lost 2 electrons.
- Starting from the ground state configuration of Yb: [Xe] 4f^14 6s^2

2. **Remove 2 electrons**:
- Remove 2 electrons from the 6s subshell:
- Resulting configuration for Yb^2+: [Xe] 4f^14

### Final Answer
- The electronic configuration of tetravalent terbium (Tb^4+) is: **[Xe] 4f^7**
- The electronic configuration of divalent ytterbium (Yb^2+) is: **[Xe] 4f^14**

### Summary
- Tetravalent Terbium (Tb^4+): **[Xe] 4f^7**
- Divalent Ytterbium (Yb^2+): **[Xe] 4f^14**