Write the number of unpaired electrons in Gd(Z=64)

Explanation

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

### Step 1: Write the Electronic Configuration
The electronic configuration of Gadolinium can be derived based on its atomic number. The atomic number 64 indicates that Gd has 64 electrons. The electronic configuration is as follows:

- The first 54 electrons fill the orbitals up to Xenon (Xe), which is the nearest noble gas.
- The next electrons fill the 4f and 5d orbitals.

Thus, the electronic configuration of Gd is:
\[ \text{[Xe]} 4f^7 5d^1 6s^2 \]

### Step 2: Analyze Each Subshell for Unpaired Electrons
Now, we will analyze the subshells to count the unpaired electrons:

1. **6s Subshell**:
- The 6s subshell has 2 electrons.
- Since both electrons are paired, it contributes **0 unpaired electrons**.

2. **5d Subshell**:
- The 5d subshell has 1 electron.
- This single electron is unpaired, contributing **1 unpaired electron**.

3. **4f Subshell**:
- The 4f subshell has 7 electrons.
- According to Hund's rule, each of the 7 electrons will occupy separate orbitals before pairing occurs. Therefore, all 7 electrons in the 4f subshell are unpaired, contributing **7 unpaired electrons**.

### Step 3: Calculate the Total Number of Unpaired Electrons
Now, we can sum the unpaired electrons from each subshell:

- From 6s: 0 unpaired electrons
- From 5d: 1 unpaired electron
- From 4f: 7 unpaired electrons

Total unpaired electrons:
\[ 0 + 1 + 7 = 8 \]

### Final Answer
The total number of unpaired electrons in Gadolinium (Gd) is **8**.

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