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

Explanation

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

### Step 1: Identify the nearest noble gas
The nearest noble gas before Gadolinium is Xenon (Xe), which has an atomic number of 54.

### Step 2: Write the electronic configuration of Xenon
The electronic configuration of Xenon is:
\[ \text{Xe} = [Kr] 4d^{10} 5s^2 5p^6 \]

### Step 3: Calculate the remaining electrons
Since Gadolinium has an atomic number of 64, we need to account for the additional electrons beyond Xenon:
\[ 64 - 54 = 10 \text{ electrons} \]

### Step 4: Fill the 4f, 5d, and 6s orbitals
The filling order for the orbitals after Xenon is:
1. 4f
2. 5d
3. 6s

For Gadolinium:
- The 4f subshell can hold a maximum of 14 electrons. Gadolinium has 7 electrons in the 4f subshell: \( 4f^7 \).
- The 5d subshell can hold a maximum of 10 electrons. Gadolinium has 1 electron in the 5d subshell: \( 5d^1 \).
- The 6s subshell can hold a maximum of 2 electrons. Gadolinium has 2 electrons in the 6s subshell: \( 6s^2 \).

### Step 5: Combine the configurations
Putting it all together, the complete electronic configuration for Gadolinium is:
\[ \text{Gd} = [Xe] 4f^7 5d^1 6s^2 \]

### Conclusion
Thus, the correct electronic configuration of Gadolinium is:
\[ [Xe] 4f^7 5d^1 6s^2 \]