What electron sublevel starts to fill after completion of the $$ 4 f $$ sublevel?

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After the $$ 4f $$ sublevel is completely filled, the next electron sublevel to begin filling is the $$ 5d $$ sublevel.

### Understanding the Order of Electron Filling

Electron orbitals fill in a specific order based on their energy levels, which is generally determined by the **Aufbau principle**. The order is primarily based on the increasing values of $$ n + l $$, where:
- $$ n $$ is the principal quantum number.
- $$ l $$ is the azimuthal quantum number.

For orbitals with the same $$ n + l $$ value, the orbital with the lower principal quantum number $$ n $$ fills first.

Here's a simplified order of orbital filling up to the $$ 5d $$ sublevel:

1. **1s**
2. **2s**
3. **2p**
4. **3s**
5. **3p**
6. **4s**
7. **3d**
8. **4p**
9. **5s**
10. **4d**
11. **5p**
12. **6s**
13. **4f**
14. **5d**

### Example: Lutetium (Lu)

Lutetium, which has an atomic number of 71, has the electron configuration:
$$ [Xe] \, 6s^2 \, 4f^{14} \, 5d^1 $$

This shows that after the $$ 4f $$ sublevel is filled, electrons begin to occupy the $$ 5d $$ sublevel.

### Summary

- **After $$ 4f $$**: The next sublevel to fill is **$$ 5d $$**.

**Answer:** After the 4f sublevel is filled, electrons begin to occupy the five d (5d) sublevel.
After the 4f sublevel is filled, electrons begin to occupy the 5d sublevel.

What electron sublevel starts to fill after completion of the \( 4 f \) sublevel?

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