The number of unpaired electrons in gadolinium (Z=64) is :

Options

A. 2
B. 6
C. 8
D. 3

Explanation

To determine the number of unpaired electrons in gadolinium (Gd), which has an atomic number of 64, we will follow these steps:

### Step 1: Write the Electronic Configuration
The first step is to write the electronic configuration of gadolinium. The electronic configuration of Gd is:
\[ \text{[Xe]} \, 6s^2 \, 4f^7 \, 5d^1 \]

### Step 2: Identify the Electrons in Each Subshell
Next, we identify the number of electrons in each subshell:
- **6s subshell**: 2 electrons
- **4f subshell**: 7 electrons
- **5d subshell**: 1 electron

### Step 3: Determine the Distribution of Electrons
Now, we need to distribute the electrons in the subshells according to Hund's rule and the Pauli exclusion principle:
- The **6s** subshell can hold a maximum of 2 electrons, and since it has 2 electrons, they will be paired.
- The **4f** subshell can hold a maximum of 14 electrons. With 7 electrons, they will fill according to Hund's rule, which states that electrons will occupy separate orbitals first before pairing up. Therefore, in the 4f subshell, there will be 7 unpaired electrons.
- The **5d** subshell has 1 electron, which will also be unpaired.

### Step 4: Count the Unpaired Electrons
Now, we count the total number of unpaired electrons:
- From the **6s** subshell: 0 unpaired electrons
- From the **4f** subshell: 7 unpaired electrons
- From the **5d** subshell: 1 unpaired electron

Adding these together gives:
\[ 0 + 7 + 1 = 8 \]

### Conclusion
The total number of unpaired electrons in gadolinium (Gd) is **8**.