The electronic configuration of gadolinium (At. No 64) is:

Options

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

Answer

To find the electronic configuration of gadolinium (Gd), which has an atomic number of 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. We will start the electronic configuration from this noble gas.

**Hint:** Always start with the nearest noble gas when writing electronic configurations.

### Step 2: Write the configuration after xenon
After xenon (Xe), we need to fill the electrons in the following order of subshells:
- 5s
- 4d
- 4f
- 5p
- 5d
- 6s

**Hint:** Remember the order of filling of orbitals based on the Aufbau principle.

### Step 3: Fill the 5s subshell
The 5s subshell can hold a maximum of 2 electrons. Therefore, we fill it completely:
- 5s²

**Hint:** Each subshell can hold a specific number of electrons: s (2), p (6), d (10), f (14).

### Step 4: Fill the 4f subshell
Next, we fill the 4f subshell. Gadolinium has 7 electrons in the 4f subshell:
- 4f⁷

**Hint:** The f subshell can hold up to 14 electrons, but for gadolinium, we only need to fill it with 7 electrons.

### Step 5: Fill the 5d subshell
After filling the 4f subshell, we move to the 5d subshell. Gadolinium has 1 electron in the 5d subshell:
- 5d¹

**Hint:** The d subshell can hold up to 10 electrons, but we only need to fill it with 1 electron for gadolinium.

### Step 6: Fill the 6s subshell
Finally, we fill the 6s subshell, which can hold 2 electrons:
- 6s²

**Hint:** Make sure to fill the s subshells after the d and f subshells when writing the electronic configuration.

### Step 7: Combine the configuration
Now, we can combine all the filled subshells to write the complete electronic configuration of gadolinium:
- Gd: [Xe] 6s² 4f⁷ 5d¹

**Hint:** The final electronic configuration should be written in the format of the nearest noble gas followed by the filled subshells.

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