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

Options

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

Explanation

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

### Step 1: Identify the nearest noble gas
The nearest noble gas to these elements is Xenon (Xe), which has an atomic number of 54. This will serve as the starting point for our electronic configurations.

### Step 2: Write the electronic configuration for Europium (Eu)
- Atomic number of Eu = 63
- Electrons beyond Xenon = 63 - 54 = 9 electrons
- The filling order of electrons follows the Aufbau principle. The 4f subshell is filled before the 5d and 6s subshells.
- Therefore, the electronic configuration for Eu is:
\[ \text{[Xe]} \, 4f^7 \, 6s^2 \]

### Step 3: Write the electronic configuration for Gadolinium (Gd)
- Atomic number of Gd = 64
- Electrons beyond Xenon = 64 - 54 = 10 electrons
- Gd has an electron configuration that includes an additional electron in the 4f subshell and one in the 5d subshell:
\[ \text{[Xe]} \, 4f^7 \, 5d^1 \, 6s^2 \]

### Step 4: Write the electronic configuration for Terbium (Tb)
- Atomic number of Tb = 65
- Electrons beyond Xenon = 65 - 54 = 11 electrons
- Tb has two additional electrons in the 4f subshell:
\[ \text{[Xe]} \, 4f^9 \, 6s^2 \]

### Final Electronic Configurations
- **Europium (Eu)**: \[ \text{[Xe]} \, 4f^7 \, 6s^2 \]
- **Gadolinium (Gd)**: \[ \text{[Xe]} \, 4f^7 \, 5d^1 \, 6s^2 \]
- **Terbium (Tb)**: \[ \text{[Xe]} \, 4f^9 \, 6s^2 \]

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