Gadolinium belongsd to 4f series. It's atomic number is 64. which of the following is the correct electronic configuration of gadolinium ?

Options

A. `[Xe]4f^7 5d^16s^2`
B. `[Xe]4f^6 5d^26s^2`
C. `[Xe] 4f^8 6d^2`
D. `[Xe]4f^9 5s^1`

Answer

To determine the correct electronic configuration of gadolinium (atomic number 64), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number**:
- Gadolinium has an atomic number of 64, which means it has 64 electrons.

2. **Determine the Noble Gas Core**:
- The nearest noble gas preceding gadolinium is xenon (Xe), which has an atomic number of 54. Therefore, we start with the electron configuration of xenon.

3. **Write the Electron Configuration Beyond Xenon**:
- After xenon, we need to fill the remaining electrons:
- Xenon (Xe): 54 electrons
- Remaining electrons to place: 64 - 54 = 10 electrons.

4. **Fill the 4f, 5d, and 6s Orbitals**:
- The order of filling orbitals according to the Aufbau principle is:
- 4f, then 5d, and then 6s.
- For gadolinium:
- Fill the 4f orbital first: 4f can hold a maximum of 14 electrons. Gadolinium has 7 electrons in the 4f subshell.
- Next, fill the 5d orbital: Gadolinium has 1 electron in the 5d subshell.
- Finally, fill the 6s orbital: Gadolinium has 2 electrons in the 6s subshell.

5. **Combine the Configurations**:
- The complete electron configuration for gadolinium becomes:
- Xe (54 electrons) + 4f^7 (7 electrons) + 5d^1 (1 electron) + 6s^2 (2 electrons).
- Thus, the electronic configuration of gadolinium is:
- **[Xe] 4f^7 5d^1 6s^2**.

### Final Answer:
The correct electronic configuration of gadolinium (atomic number 64) is:
**[Xe] 4f^7 5d^1 6s^2**.