To determine which set of quantum numbers is not possible, we need to analyze the four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).
### Step-by-Step Solution:
1. **Understanding Quantum Numbers**:
- **Principal Quantum Number (n)**: This number indicates the main energy level of an electron in an atom. It can take positive integer values (n = 1, 2, 3, ...).
- **Azimuthal Quantum Number (l)**: This number describes the subshell and can take values from 0 to (n-1). For example, if n = 3, then l can be 0, 1, or 2.
- **Magnetic Quantum Number (m_l)**: This number indicates the orientation of the orbital and can take values from -l to +l, including zero.
- **Spin Quantum Number (m_s)**: This number describes the spin of the electron and can be either +1/2 or -1/2.
2. **Analyzing the Options**:
- **Option 1**: n = 3, l = 0, m_l = 0, m_s = -1/2
- Here, n = 3 is valid, l = 0 is valid (s orbital), m_l = 0 is valid, and m_s = -1/2 is valid. This set is possible.
- **Option 2**: n = 3, l = 2, m_l = 0, m_s = +1/2
- Here, n = 3 is valid, l = 2 is valid (d orbital), m_l = 0 is valid, and m_s = +1/2 is valid. This set is possible.
- **Option 3**: n = 3, l = 3, m_l = 0, m_s = -1/2
- Here, n = 3 is valid, but l = 3 is not valid because l must be less than n (l can be 0, 1, or 2 when n = 3). Therefore, this set is **not possible**.
- **Option 4**: n = 4, l = 2, m_l = -2, m_s = +1/2
- Here, n = 4 is valid, l = 2 is valid (d orbital), m_l = -2 is valid (since m_l can range from -l to +l), and m_s = +1/2 is valid. This set is possible.
3. **Conclusion**:
- The only set of quantum numbers that is not possible is **Option 3: n = 3, l = 3, m_l = 0, m_s = -1/2**.
### Final Answer:
**Option 3** is the set of quantum numbers that is not possible.
