Which of the following sets of quantum number is not possible

Options

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

Answer

To determine which set of quantum numbers is not possible, we need to analyze each set based on the rules governing quantum numbers.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number (n) indicates the energy level 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 (m_l) can take integer values from -l to +l.
- The spin quantum number (m_s) can be either +1/2 or -1/2.

2. **Analyzing Each Option**:
- Let's denote the quantum numbers for each option as (n, l, m_l, m_s).

3. **Option A**: (3, 2, 1, +1/2)
- n = 3, l = 2 (valid since l can be 0, 1, or 2 for n=3)
- m_l = 1 (valid since m_l can range from -2 to +2)
- m_s = +1/2 (valid)
- **Conclusion**: This set is possible.

4. **Option B**: (2, 1, -1, -1/2)
- n = 2, l = 1 (valid since l can be 0 or 1 for n=2)
- m_l = -1 (valid since m_l can range from -1 to +1)
- m_s = -1/2 (valid)
- **Conclusion**: This set is possible.

5. **Option C**: (3, 2, 0, -1/2)
- n = 3, l = 2 (valid since l can be 0, 1, or 2 for n=3)
- m_l = 0 (valid since m_l can range from -2 to +2)
- m_s = -1/2 (valid)
- **Conclusion**: This set is possible.

6. **Option D**: (3, 2, 3, +1/2)
- n = 3, l = 2 (valid since l can be 0, 1, or 2 for n=3)
- m_l = 3 (not valid since m_l can only range from -2 to +2)
- **Conclusion**: This set is NOT possible.

### Final Answer:
The set of quantum numbers that is not possible is **Option D**.