The outer electronic configuration of Gd (At.No. 64) is

Options

A. `4f^(3)5d^(5)6s^(2)`
B. `4f^(8)5d^(6)6s^(2)`
C. `4f^(4)5d^(4)6s^(2)`
D. `4f^(7)5d^(1)6s^(2)`

Explanation

To determine the outer electronic configuration of Gadolinium (Gd) with atomic number 64, we can follow these steps:

### Step 1: Identify the Atomic Number
The atomic number of Gadolinium (Gd) is 64. This means that a neutral Gd atom has 64 electrons.

### Step 2: Write the Electronic Configuration
We start by filling the electron orbitals according to the Aufbau principle, which states that electrons fill orbitals starting from the lowest energy level to the highest.

1. **Fill the 1s orbital**: 2 electrons
2. **Fill the 2s orbital**: 2 electrons
3. **Fill the 2p orbital**: 6 electrons
4. **Fill the 3s orbital**: 2 electrons
5. **Fill the 3p orbital**: 6 electrons
6. **Fill the 4s orbital**: 2 electrons
7. **Fill the 3d orbital**: 10 electrons
8. **Fill the 4p orbital**: 6 electrons
9. **Fill the 5s orbital**: 2 electrons
10. **Fill the 4d orbital**: 10 electrons
11. **Fill the 5p orbital**: 6 electrons
12. **Fill the 6s orbital**: 2 electrons
13. **Fill the 4f orbital**: 14 electrons (this is where we start filling the f-block)
14. **Fill the 5d orbital**: 1 electron (since Gd has a total of 64 electrons)

### Step 3: Count the Electrons
Now, let's count the electrons:
- From 1s to 5p, we have filled 54 electrons.
- The 6s orbital has 2 electrons, bringing the total to 56.
- The 4f orbital has 7 electrons (since we need a total of 64 electrons, and we have already accounted for 56).
- The 5d orbital has 1 electron.

### Step 4: Write the Outer Electronic Configuration
The outer electronic configuration of Gd can be summarized as:
- 4f: 7 electrons
- 5d: 1 electron
- 6s: 2 electrons

Thus, the complete outer electronic configuration of Gadolinium (Gd) is:
**[Xe] 4f^7 5d^1 6s^2**

### Final Answer
The outer electronic configuration of Gd (Atomic Number 64) is:
**[Xe] 4f^7 5d^1 6s^2**

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