The `f`-block elements of the periodic table contains those element in which

Options

A. Only `4f` orbitals are progressively filled in `6th` period.
B. Only `5f` orbitals are progressively filled in `7th` period.
C. `4f` and `5f` orbitals are progressivley filled in `6th` and `7th` period respectively.
D. none

Explanation

To solve the question regarding the `f`-block elements of the periodic table, we need to understand the electronic configuration of these elements and identify the correct statement among the provided options.

### Step-by-Step Solution:

1. **Identify the `f`-block Elements**:
- The `f`-block elements are located in the periodic table and include the lanthanides and actinides. These elements are characterized by the filling of `f` orbitals.

2. **General Electronic Configuration**:
- The general electronic configuration for `f`-block elements can be written as:
\[ [\text{Noble Gas}] \, (n-2)f^{1-14} \, (n-1)d^{0-1} \, ns^2 \]
- Here, `n` represents the principal quantum number.

3. **Determine the Periods**:
- The `f`-block elements start from the 6th period of the periodic table.
- For the 6th period, `n = 6`, which means the `4f` orbital is filled.
- For the 7th period, `n = 7`, which means the `5f` orbital is filled.

4. **Filling of `f` Orbitals**:
- In the 6th period, the `4f` orbitals are progressively filled.
- In the 7th period, the `5f` orbitals are progressively filled.
- Therefore, both `4f` and `5f` orbitals are involved in the `f`-block elements.

5. **Evaluate the Options**:
- The options provided need to be evaluated based on the information gathered:
- **Option 1**: Only `4f` orbitals are progressively filled in the 6th period. (Incorrect)
- **Option 2**: Only `5f` orbitals are progressively filled in the 7th period. (Incorrect)
- **Option 3**: `4f` and `5f` orbitals are progressively filled in the 6th and 7th periods respectively. (Correct)
- **Option 4**: None of the above. (Incorrect)

6. **Conclusion**:
- The correct answer is **Option 3**: `4f` and `5f` orbitals are progressively filled in the 6th and 7th periods respectively.