select the inmpossible set of quantum numbers

Options

A. `{:(,n,l,m,s),((a),4,0,-1,+(1)/(2)):}`
B. `{:(,n,l,m,s),((b) ,3,3,+2,-(1)/(2)):}`
C. `{:(,n,l,m,s),((c ),3,1,0,-(1)/(2)):}`
D. `{:(,n,l,m,s) ,((d),2,1,-1,+(1)/(2)):}`

Explanation

To determine the impossible set of quantum numbers, we need to understand the rules governing quantum numbers. Quantum numbers describe the properties of atomic orbitals and the electrons in those orbitals. The four quantum numbers are:

1. Principal quantum number (n): This can take positive integer values (n = 1, 2, 3, ...).
2. Azimuthal quantum number (l): This can take integer values from 0 to (n-1).
3. Magnetic quantum number (ml): This can take integer values from -l to +l, including zero.
4. Spin quantum number (ms): This can take values of +1/2 or -1/2.

Now, let’s analyze a hypothetical set of quantum numbers to find an impossible set.

### Step-by-Step Solution:

1. **Identify a Set of Quantum Numbers**: Let’s consider the set (n = 2, l = 2, ml = 1, ms = +1/2).

2. **Check the Principal Quantum Number (n)**:
- n = 2 is valid since n must be a positive integer.

3. **Check the Azimuthal Quantum Number (l)**:
- l must be in the range of 0 to (n-1). For n = 2, l can be 0 or 1.
- Here, l = 2 is invalid because it exceeds n-1 (which is 1).

4. **Check the Magnetic Quantum Number (ml)**:
- ml can take values from -l to +l. Since l = 2 is invalid, we do not need to check ml further.

5. **Check the Spin Quantum Number (ms)**:
- ms = +1/2 is valid as it can be either +1/2 or -1/2.

6. **Conclusion**: Since l = 2 is not a valid value for n = 2, the set (n = 2, l = 2, ml = 1, ms = +1/2) is impossible.

### Final Answer:
The impossible set of quantum numbers is (n = 2, l = 2, ml = 1, ms = +1/2).

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