Which of the following sets of quantum number is not possible

Options

A. `n=3,1=+2,m_(1)=0,m_(s)=+1//2`
B. `n=3,1=0,m_(1)=0,m_(s)=-1//2`
C. `n=3,1=0,m_(1)=-1,m_(s)=+1//2`
D. `n=3,1=1,m_(1)=0,m_(s)=+1//2`

Answer

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

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

Let's break down the steps to find the set of quantum numbers that is not possible.

### Step 1: Identify the given quantum numbers
We are given that the principal quantum number \( n = 3 \).

### Step 2: Determine possible values for \( l \)
The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \). Therefore, for \( n = 3 \):
- Possible values for \( l \) are \( 0, 1, 2 \).

### Step 3: Determine possible values for \( m \)
The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \). Thus:
- If \( l = 0 \), then \( m = 0 \).
- If \( l = 1 \), then \( m = -1, 0, +1 \).
- If \( l = 2 \), then \( m = -2, -1, 0, +1, +2 \).

### Step 4: Analyze the provided sets of quantum numbers
Let's analyze the sets of quantum numbers provided in the question (assuming we have three sets to analyze):

1. **Set 1:** \( n = 3, l = 2, m = 0 \)
- Valid because \( l \) is within the range (0 to 2) and \( m \) is within the range (-2 to 2).

2. **Set 2:** \( n = 3, l = 0, m = 0 \)
- Valid because \( l = 0 \) allows \( m = 0 \).

3. **Set 3:** \( n = 3, l = 1, m = 0 \)
- Valid because \( l = 1 \) allows \( m = 0 \).

### Step 5: Identify the invalid set
From the analysis, we find that all sets provided are valid. However, if we consider a hypothetical set such as \( n = 3, l = 2, m = 3 \):
- This would be invalid because \( m \) cannot exceed \( l \).

### Conclusion
In the analysis, we found that the second set \( n = 3, l = 0, m = 0 \) is valid, but if there were a set like \( n = 3, l = 2, m = 3 \), that would be invalid. Therefore, based on the original question, the second set is the one that is not possible.