To determine which of the given sets of quantum numbers is not possible, we need to analyze each set based on the rules governing quantum numbers. The three quantum numbers in question are:
1. **Principal Quantum Number (n)**: Indicates the energy level and size of the orbital.
2. **Azimuthal Quantum Number (l)**: Indicates the shape of the orbital. The values of l range from 0 to (n-1).
3. **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital. The values of m range from -l to +l.
Let's analyze each option step by step:
### Step 1: Analyze the first set of quantum numbers (n=3, l=0, m=0)
- **n = 3**: This is valid as n can be any positive integer.
- **l = 0**: This is valid because l can take values from 0 to (n-1), and since n=3, l can be 0, 1, or 2.
- **m = 0**: This is valid because for l=0 (s orbital), the only possible value for m is 0.
**Conclusion**: This set is possible.
### Step 2: Analyze the second set of quantum numbers (n=3, l=1, m=-1)
- **n = 3**: Valid.
- **l = 1**: Valid (l can be 0, 1, or 2 when n=3).
- **m = -1**: Valid because for l=1 (p orbital), m can be -1, 0, or +1.
**Conclusion**: This set is possible.
### Step 3: Analyze the third set of quantum numbers (n=2, l=0, m=1)
- **n = 2**: Valid.
- **l = 0**: Valid (l can be 0 or 1 when n=2).
- **m = 1**: Not valid because for l=0 (s orbital), the only possible value for m is 0.
**Conclusion**: This set is NOT possible.
### Step 4: Analyze the fourth set of quantum numbers (n=2, l=1, m=-1)
- **n = 2**: Valid.
- **l = 1**: Valid (l can be 0 or 1 when n=2).
- **m = -1**: Valid because for l=1 (p orbital), m can be -1, 0, or +1.
**Conclusion**: This set is possible.
### Final Answer
The set of quantum numbers that is **not possible** is **(n=2, l=0, m=1)**.
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