Which of the following set of quantum numbers is not valid.

Options

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

Explanation

To determine which set of quantum numbers is not valid, we need to analyze each option based on the rules governing quantum numbers. The quantum numbers are:

1. **Principal quantum number (n)**: Can be any positive integer (1, 2, 3,...).
2. **Azimuthal quantum number (l)**: Can take values from 0 to (n-1).
3. **Magnetic quantum number (m)**: Can take values from -l to +l.
4. **Spin quantum number (s)**: Can be either +1/2 or -1/2.

Now, let's evaluate each option step-by-step.

### Step 1: Evaluate Option A
- **n = 3**
- **l = 2** (valid since l can be 0, 1, or 2 for n=3)
- **m = 2** (valid since m can be -2, -1, 0, 1, 2 for l=2)
- **s = +1/2** (valid)

**Conclusion**: Option A is valid.

### Step 2: Evaluate Option B
- **n = 2**
- **l = 0** (valid since l can be 0 for n=2)
- **m = 0** (valid since m can be 0 for l=0)
- **s = -1/2** (valid)

**Conclusion**: Option B is valid.

### Step 3: Evaluate Option C
- **n = 4**
- **l = 2** (valid since l can be 0, 1, 2, or 3 for n=4)
- **m = -1** (valid since m can be -2, -1, 0, 1, 2 for l=2)
- **s = +1/2** (valid)

**Conclusion**: Option C is valid.

### Step 4: Evaluate Option D
- **n = 4**
- **l = 3** (valid since l can be 0, 1, 2, or 3 for n=4)
- **m = 4** (invalid since m can only take values from -l to +l, which means for l=3, m can be -3, -2, -1, 0, 1, 2, 3)
- **s = -1/2** (valid)

**Conclusion**: Option D is not valid because m cannot be greater than l.

### Final Answer
The set of quantum numbers that is not valid is **Option D**.

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