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 Gadolinium (Gd) with atomic number 64, we need to determine the number of unpaired electrons and the sum of their spins. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the electronic configuration of Gadolinium (Gd)
- Gadolinium has an atomic number of 64.
- The electronic configuration can be written as:
- \( \text{[Xe]} 6s^2 5d^1 4f^7 \)

### Step 2: Identify the distribution of electrons in the orbitals
- In the electronic configuration:
- The 6s orbital has 2 electrons (paired).
- The 5d orbital has 1 electron (unpaired).
- The 4f orbital has 7 electrons.

### Step 3: Determine the number of unpaired electrons in the 4f orbital
- The 4f subshell can hold a maximum of 14 electrons (7 orbitals, each can hold 2 electrons).
- With 7 electrons in the 4f subshell, the filling will be:
- 1 electron in each of the 7 orbitals (due to Hund's rule) before any pairing occurs.
- Therefore, all 7 electrons in the 4f subshell are unpaired.

### Step 4: Count the total number of unpaired electrons
- From the 6s orbital: 0 unpaired electrons (2 paired).
- From the 5d orbital: 1 unpaired electron.
- From the 4f orbital: 7 unpaired electrons.
- Total unpaired electrons = 0 + 1 + 7 = 8 unpaired electrons.

### Step 5: Calculate the sum of the spins of the unpaired electrons
- Each unpaired electron has a spin of \( +\frac{1}{2} \).
- Therefore, the sum of the spins for 8 unpaired electrons:
- Sum of spins = \( 8 \times \frac{1}{2} = 4 \).

### Final Answer
- Gd (64) has **8 unpaired electrons** with a sum of spin of **4**.