Which of the following set of quantum numbers is not consistent with the theory ?

Options

A. `n=2,l=1,m=0,s=+1//2`
B. `n=4,l-3,m=2,s=-1//2`
C. `n=3,l=2,m=3,s=-1//2`
D. `n=4,l=3,m=3,s=+1//2`

Explanation

To determine which set of quantum numbers is not consistent with the theory, we need to analyze each set of quantum numbers provided in the options. The quantum numbers consist of:

1. Principal quantum number (n)
2. Azimuthal quantum number (l)
3. Magnetic quantum number (m)
4. Spin quantum number (s)

Let's go through the options step by step:

### Step 1: Analyze each option

**Option A:**
- n = 2
- l = 1 (valid since l can be 0 to n-1)
- m = 0 (valid since m can range from -l to +l)
- s = +1/2 (valid since s can be +1/2 or -1/2)

**Conclusion:** This set is consistent with the theory.

**Option B:**
- n = 4
- l = 3 (valid since l can be 0 to n-1)
- m = -3 (valid since m can range from -l to +l)
- s = -1/2 (valid since s can be +1/2 or -1/2)

**Conclusion:** This set is consistent with the theory.

**Option C:**
- n = 3
- l = 2 (valid since l can be 0 to n-1)
- m = 3 (invalid since m can only range from -l to +l, which is -2 to +2)
- s = +1/2 or -1/2 (valid)

**Conclusion:** This set is NOT consistent with the theory because m cannot be 3 when l is 2.

**Option D:**
- n = 4
- l = 3 (valid since l can be 0 to n-1)
- m = 2 (valid since m can range from -l to +l)
- s = +1/2 (valid since s can be +1/2 or -1/2)

**Conclusion:** This set is consistent with the theory.

### Final Answer:
The set of quantum numbers that is not consistent with the theory is **Option C**.

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