To determine the impossible set of quantum numbers, we need to analyze each set of quantum numbers based on the rules governing quantum mechanics. Quantum numbers describe the properties of atomic orbitals and the electrons in those orbitals. The four quantum numbers 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 and can take values from 0 to (n-1).
3. Magnetic quantum number (m): Indicates the orientation of the orbital and can take values from -l to +l.
4. Spin quantum number (s): Indicates the spin of the electron and can be either +1/2 or -1/2.
Now, let's analyze the given options one by one:
### Step 1: Analyze Option 1
- **n = 2, l = 0, m = 0, s = +1/2**
- Here, n = 2 means we are in the second energy level.
- l = 0 corresponds to the s subshell.
- For l = 0, m can only be 0.
- s can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Step 2: Analyze Option 2
- **n = 2, l = 1, m = 0, s = +1/2**
- n = 2 indicates the second energy level.
- l = 1 corresponds to the p subshell.
- For l = 1, m can be -1, 0, or +1.
- s can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Step 3: Analyze Option 3
- **n = 2, l = 0, m = 1, s = -1/2**
- n = 2 indicates the second energy level.
- l = 0 corresponds to the s subshell.
- For l = 0, m can only be 0 (not 1).
- s can be +1/2 or -1/2.
- **Conclusion**: This set is impossible because m cannot be 1 when l is 0.
### Step 4: Analyze Option 4
- **n = 3, l = 1, m = -1, s = -1/2**
- n = 3 indicates the third energy level.
- l = 1 corresponds to the p subshell.
- For l = 1, m can be -1, 0, or +1.
- s can be +1/2 or -1/2.
- **Conclusion**: This set is possible.
### Final Conclusion
The impossible set of quantum numbers is **Option 3: n = 2, l = 0, m = 1, s = -1/2**.
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