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

Options

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

Answer

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 electron configuration up to xenon
- The electron configuration of xenon (Xe) is:
\[ \text{Xe: } [Kr] 4s^2 3d^{10} 4p^6 \]

### Step 3: Determine the remaining electrons
- Gadolinium has a total of 64 electrons. Since xenon accounts for 54 electrons, we have:
\[ 64 - 54 = 10 \text{ electrons remaining} \]

### Step 4: Fill the 4f, 5d, and 6s subshells
- Gadolinium is in the 4f series, so we will fill the 4f subshell first. The 4f subshell can hold a maximum of 14 electrons.
- To achieve a stable electronic configuration, we can fill the 4f subshell with 7 electrons and then place 1 electron in the 5d subshell. The remaining 2 electrons will go into the 6s subshell.

### Step 5: Write the complete electronic configuration
- Therefore, the complete electronic configuration of gadolinium (Gd) can be written as:
\[ \text{Gd: } [Xe] 4f^7 5d^1 6s^2 \]

### Conclusion
- The correct electronic configuration for gadolinium is:
\[ [Xe] 4f^7 5d^1 6s^2 \]