The electronic configuration of gadolinium (atomic number 64) is:

Options

A. `(Xe) 4f^8 5d^9 6s^2`
B. `(Xe) 4f^7 5d^1 6s^2`
C. `(Xe) 4f^7 5d^3 6s^2`
D. `(Xe) 4f^6 5d^2 6s^2 `

Explanation

To determine the 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. This means it has 64 electrons.

2. **Determine the Previous Noble Gas**:
The noble gas preceding gadolinium in the periodic table is xenon (Xe), which has an atomic number of 54. Therefore, we can start the electronic configuration from xenon.

3. **Calculate Remaining Electrons**:
After xenon, we have 64 - 54 = 10 electrons left to distribute in the subshells.

4. **Understand the Filling Order**:
The order of filling the subshells follows the Aufbau principle. For lanthanides like gadolinium, the 4f subshell is filled before the 5d and 6s subshells.

5. **Fill the Electrons**:
- The 4f subshell can hold a maximum of 14 electrons.
- The 5d subshell can hold a maximum of 10 electrons.
- The 6s subshell can hold a maximum of 2 electrons.

To achieve a stable configuration, gadolinium has:
- 7 electrons in the 4f subshell (4f^7)
- 1 electron in the 5d subshell (5d^1)
- 2 electrons in the 6s subshell (6s^2)

6. **Write the Complete Electronic Configuration**:
Combining all the filled subshells, the electronic configuration of gadolinium is:
\[ [Xe] 6s^2 4f^7 5d^1 \]

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

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