An element with atomic number 64 will have the electronic configuration

Options

A. `[Xe]6s^2 4f^8`
B. `[Xe]6s^2 4f^7 5d^1`
C. `[Xe]4f^(10)`
D. `[Xe]6s^2 4f^7 5p^1`

Answer

To determine the electronic configuration of an element with atomic number 64, we can follow these steps:

### Step 1: Identify the Element
The element with atomic number 64 is Gadolinium (Gd).

### Step 2: Determine the Electron Configuration Order
The order of filling the atomic orbitals is based on the Aufbau principle. The order is as follows:
1. 1s
2. 2s
3. 2p
4. 3s
5. 3p
6. 4s
7. 3d
8. 4p
9. 4d
10. 4f
11. 5s
12. 5p
13. 5d
14. 6s
15. 6p

### Step 3: Fill the Orbitals
- The first 54 electrons fill up to the noble gas configuration of Xenon (Xe), which is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ (Total = 54 electrons).

- After Xenon, we need to fill the remaining 10 electrons for Gadolinium (64 - 54 = 10).

### Step 4: Fill the 4f and 5d Orbitals
- The next orbitals to fill are the 4f and 5d orbitals. The filling order after Xenon is:
- 4f (which can hold a maximum of 14 electrons)
- 5d (which can hold a maximum of 10 electrons)
- 6s (which can hold a maximum of 2 electrons)

- For Gadolinium, we fill the 4f subshell first:
- 4f: 7 electrons (4f⁷)

- Then we fill the 5d subshell:
- 5d: 1 electron (5d¹)

- Finally, we fill the 6s subshell:
- 6s: 2 electrons (6s²)

### Step 5: Write the Complete Electron Configuration
Combining all the filled orbitals, the complete electron configuration for Gadolinium (atomic number 64) is:
\[ \text{[Xe]} 4f^7 5d^1 6s^2 \]

### Final Answer
The electronic configuration of the element with atomic number 64 (Gadolinium) is:
\[ \text{[Xe]} 4f^7 5d^1 6s^2 \]

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