Gd (64) has ………..unpaired electrons with sum of spin ………..

Options

A. 7,3.5
B. 8,3
C. 6,3
D. 8,4

Answer

To solve the question regarding the number of unpaired electrons and the sum of their spins for Gadolinium (Gd, atomic number 64), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Electronic Configuration of Gadolinium (Gd)**:
- The atomic number of Gadolinium is 64. The electronic configuration can be derived as follows:
- Gd: [Xe] 6s² 4f⁷ 5d¹
- Here, [Xe] represents the electron configuration of Xenon, which accounts for the first 54 electrons.

2. **Determine the Distribution of Electrons**:
- In the outermost shells:
- 6s²: Both electrons are paired.
- 4f⁷: There are 7 electrons in the f subshell. The f subshell can hold a maximum of 14 electrons, and since there are 7 electrons, they will occupy separate orbitals with one electron each, leading to 7 unpaired electrons.
- 5d¹: There is 1 electron in the d subshell, which is also unpaired.

3. **Count the Total Number of Unpaired Electrons**:
- From the above distribution:
- Unpaired electrons from 4f: 7
- Unpaired electrons from 5d: 1
- Total unpaired electrons = 7 (from 4f) + 1 (from 5d) = 8 unpaired electrons.

4. **Calculate the Sum of Spin Quantum Numbers**:
- Each unpaired electron contributes a spin of +1/2.
- Therefore, for 8 unpaired electrons, the sum of their spins is:
- Sum of spins = Number of unpaired electrons × Spin per electron
- Sum of spins = 8 × (1/2) = 4.

5. **Final Answer**:
- Gadolinium (Gd) has **8 unpaired electrons** and the **sum of spin is 4**.

### Summary:
- Gadolinium (Gd) has **8 unpaired electrons** with a **sum of spin equal to 4**.