Select the correct set (s) of quantum numbers

Options

A. `n=3, l=0, m_(l)=-1`
B. `n=3, l=3, m_(l)=-2`
C. `n=3, l=2, m_(l)=-2`
D. `n=3, l=1, m_(l)=0`

Explanation

To solve the question of selecting the correct set(s) of quantum numbers, we will analyze the quantum numbers based on the rules governing them.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The principal quantum number (n) indicates the energy level of an electron and can take positive integer values (1, 2, 3, ...).
- The azimuthal quantum number (l) determines the shape of the orbital and can take values from 0 to (n-1).
- The magnetic quantum number (ml) specifies the orientation of the orbital and can take values from -l to +l, including zero.

2. **Evaluate Each Option**:
- **Option A**: n = 3, l = 0, ml = -1
- For n = 3, l can be 0, 1, or 2. Since l = 0 is valid, ml must be 0 (the only value for l = 0). Thus, this option is **not valid**.

- **Option B**: n = 3, l = 3, ml = 0
- For n = 3, l can only be 0, 1, or 2. Since l = 3 is not valid, this option is **not valid**.

- **Option C**: n = 3, l = 2, ml = -2
- For n = 3, l = 2 is valid. The possible values for ml when l = 2 are -2, -1, 0, 1, 2. Since ml = -2 is included, this option is **valid**.

- **Option D**: n = 3, l = 1, ml = -1
- For n = 3, l = 1 is valid. The possible values for ml when l = 1 are -1, 0, 1. Since ml = -1 is included, this option is **valid**.

3. **Conclusion**:
- The valid sets of quantum numbers are **Option C** and **Option D**.

### Final Answer:
The correct sets of quantum numbers are **Option C** and **Option D**.