To determine which set of quantum numbers is impossible for an electron, we need to analyze each set based on the rules governing quantum numbers:
1. **Principal Quantum Number (n)**: This number can take positive integer values (1, 2, 3, ...). It represents the energy level and size of the orbital.
2. **Azimuthal Quantum Number (l)**: For a given value of n, l can take integer values from 0 to (n-1). This number describes the shape of the orbital.
3. **Magnetic Quantum Number (ml)**: For a given value of l, ml can take integer values from -l to +l, including 0. This number describes the orientation of the orbital in space.
4. **Spin Quantum Number (ms)**: This number can be either +1/2 or -1/2, representing the two possible orientations of the electron's spin.
Now, let's analyze the given sets of quantum numbers one by one:
### Set 1: n = 1, l = 0, ml = 0, ms = +1/2
- For n = 1, l can be 0 (since l ranges from 0 to n-1, which is 0).
- For l = 0, ml can only be 0.
- ms can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Set 2: n = 9, l = 7, ml = -6, ms = -1/2
- For n = 9, l can range from 0 to 8 (n-1).
- l = 7 is valid.
- For l = 7, ml can range from -7 to +7. Thus, ml = -6 is valid.
- ms can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Set 3: n = 2, l = 1, ml = 0, ms = +1/2
- For n = 2, l can be 0 or 1 (0 to n-1).
- l = 1 is valid.
- For l = 1, ml can range from -1 to +1. Thus, ml = 0 is valid.
- ms can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Set 4: n = 3, l = 2, ml = -3, ms = +1/2
- For n = 3, l can be 0, 1, or 2 (0 to n-1).
- l = 2 is valid.
- For l = 2, ml can range from -2 to +2. Thus, ml = -3 is **not valid**.
- ms can be +1/2 or -1/2.
- **Conclusion**: This set is impossible.
### Final Answer:
The set of quantum numbers that is impossible for an electron is **n = 3, l = 2, ml = -3, ms = +1/2**.
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