Which set of quantum numbers is not consistent with theory?

Options

A. `n=2,l=1,m=0,s= - (1)/(2)`
B. `n= 4 , l=3,m=2,s=- (1)/(2)`
C. `n= 3 , l=2 , m=3 , s= + (1)/(2)`
D. `n=4,l=3,m=3,s= + (1)/(2)`

Answer

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

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- **Principal Quantum Number (n)**: Indicates the main energy level of an electron in an atom. It can take positive integer values (1, 2, 3,...).
- **Azimuthal Quantum Number (l)**: Indicates the subshell and can take values from 0 to (n-1).
- **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital and can take values from -l to +l.
- **Spin Quantum Number (s)**: Indicates the spin of the electron and can be either +1/2 or -1/2.

2. **Analyzing Each Option**:
- **Option A**: n = 2, l = 1, m = 0, s = -1/2
- For n = 2, l can be 0 or 1 (valid).
- For l = 1, m can be -1, 0, +1 (valid).
- s = -1/2 is valid.
- **Conclusion**: This set is consistent with theory.

- **Option B**: n = 4, l = 3, m = 2, s = -1/2
- For n = 4, l can be 0, 1, 2, or 3 (valid).
- For l = 3, m can be -3, -2, -1, 0, +1, +2, +3 (valid).
- s = -1/2 is valid.
- **Conclusion**: This set is consistent with theory.

- **Option C**: n = 3, l = 2, m = 3, s = +1/2
- For n = 3, l can be 0, 1, or 2 (valid).
- For l = 2, m can be -2, -1, 0, +1, +2 (invalid since m cannot be 3).
- **Conclusion**: This set is not consistent with theory.

- **Option D**: n = 4, l = 3, m = 3, s = +1/2
- For n = 4, l can be 0, 1, 2, or 3 (valid).
- For l = 3, m can be -3, -2, -1, 0, +1, +2, +3 (valid).
- s = +1/2 is valid.
- **Conclusion**: This set is consistent with theory.

3. **Final Answer**:
- The set of quantum numbers that is not consistent with theory is **Option C**: n = 3, l = 2, m = 3, s = +1/2.