For 1=3, which value of m is not possible?

Options

A. 4
B. 0
C. `-3`
D. `-1`

Answer

To determine which value of \( m \) is not possible when \( l = 3 \), we need to understand the relationship between the azimuthal quantum number \( l \) and the magnetic quantum number \( m \).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The azimuthal quantum number \( l \) can take on integer values starting from 0 up to \( n-1 \), where \( n \) is the principal quantum number.
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \).

2. **Given Value of \( l \)**:
- In this case, we have \( l = 3 \).

3. **Determining Possible Values of \( m \)**:
- The possible values of \( m \) when \( l = 3 \) are:
\[ m = -l, -l + 1, \ldots, 0, \ldots, l - 1, l \]
- This translates to:
\[ m = -3, -2, -1, 0, 1, 2, 3 \]

4. **Counting the Values**:
- The total values of \( m \) are:
- \( -3 \)
- \( -2 \)
- \( -1 \)
- \( 0 \)
- \( 1 \)
- \( 2 \)
- \( 3 \)
- This gives us a total of 7 possible values.

5. **Identifying the Not Possible Value**:
- Since \( m \) can only take values from \( -3 \) to \( 3 \), any value outside this range is not possible.
- For example, \( m = 4 \) is not a valid value for \( l = 3 \).

### Conclusion:
The value of \( m \) that is not possible when \( l = 3 \) is **4**.