The electronic configuration of Eu (Atomic No. 63), Gd (Atomic No. 64) and Tb (Atomic No. 65) are:

Options

A. `[Xe4f^(7)6s^(2), [Xej4f^(7)5d^(1) 6s^(2)` and `[Xej4f^(9)6s^(2)`
B. `[Xe]4f^(7)6s^(2), [Xe]4f^(8)6s^(2)` and `[Xe]4f^(8)5d^(1)6s^(2)`
C. `[Xe]4f^(6)5d^(1)6s^(2), [Xe]4f^(7)5f^(1)` and `[Xe]4f^(9)6s^(2)`
D. `[Xe4f^(6)5d^(1)6s^(2), [Xe]4f^(7)5d^(1)6s^(2)` and `[Xe]4f^(8)5d^(1)6s^(2)`

Answer

To find the electronic configurations of Europium (Eu), Gadolinium (Gd), and Terbium (Tb), we will follow these steps:

### Step 1: Understand the Aufbau Principle
The Aufbau principle states that electrons fill atomic orbitals in order of increasing energy levels. The order of filling is generally as follows:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p.

### Step 2: Write the Electronic Configuration for Europium (Eu)
- **Atomic Number of Eu**: 63
- We start filling from 1s up to 6s, and then we fill the f-orbitals.
- The configuration can be written as:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 4f⁷
- To express it in terms of the nearest noble gas (Xe), we have:
- **Electronic Configuration of Eu**: [Xe] 4f⁷ 6s²

### Step 3: Write the Electronic Configuration for Gadolinium (Gd)
- **Atomic Number of Gd**: 64
- Following the same filling order:
- The configuration will be:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 4f⁷ 5d¹
- In terms of the nearest noble gas (Xe), we write:
- **Electronic Configuration of Gd**: [Xe] 4f⁷ 5d¹ 6s²

### Step 4: Write the Electronic Configuration for Terbium (Tb)
- **Atomic Number of Tb**: 65
- Continuing from Gd:
- The configuration will be:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 4f⁸
- In terms of the nearest noble gas (Xe), we write:
- **Electronic Configuration of Tb**: [Xe] 4f⁸ 6s²

### Summary of Electronic Configurations
- **Europium (Eu)**: [Xe] 4f⁷ 6s²
- **Gadolinium (Gd)**: [Xe] 4f⁷ 5d¹ 6s²
- **Terbium (Tb)**: [Xe] 4f⁸ 6s²