Which set of quantum numbers is not possible ?

Options

A. `{:(n,l,m," s"),(3,2,0,+1//2):}`
B. `{:(n,l,m," s"),(2,2,1,+1//2):}`
C. `{:(n,l,m," s"),(1,0,0,-1//2):}`
D. `{:(n,l,m," s"),(3,2,-2,+1//2):}`

Explanation

To determine which set of quantum numbers is not possible, we need to understand the rules governing the quantum numbers:

1. **Principal Quantum Number (n)**: This can take positive integer values (1, 2, 3, ...).
2. **Azimuthal Quantum Number (l)**: This can take values from 0 to (n-1).
3. **Magnetic Quantum Number (ml)**: This can take values from -l to +l, including zero.
4. **Spin Quantum Number (ms)**: This can be either +1/2 or -1/2.

Now, let's analyze each option step by step:

### Step 1: Analyze Option 1
- Given: n = 3, l = 2, ml = 0
- Here, l can take values from 0 to (n-1) = 2.
- Since l = 2 is valid, we check ml:
- ml can range from -l to +l, which means ml can be -2, -1, 0, 1, or 2.
- This option is valid.

### Step 2: Analyze Option 2
- Given: n = 2, l = 2
- Here, l must be less than n, so l can only be 0 or 1 (0 to n-1).
- Since l = 2 is not valid, this option is not possible.

### Step 3: Analyze Option 3
- Given: n = 1, l = 0, ml = 0
- Here, l can take values from 0 to (n-1) = 0.
- Since l = 0 is valid, we check ml:
- ml can only be 0 when l = 0.
- This option is valid.

### Step 4: Analyze Option 4
- Given: n = 3, l = 2, ml = -2
- Here, l can take values from 0 to (n-1) = 2.
- Since l = 2 is valid, we check ml:
- ml can range from -2 to +2, which includes -2.
- This option is valid.

### Conclusion
The only invalid set of quantum numbers is from **Option 2**: (n=2, l=2).