For `n=4` , which one of the following values of l is not possible ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine which value of the azimuthal quantum number \( l \) is not possible for a principal quantum number \( n = 4 \), we will follow these steps:

### Step 1: Understand the relationship between \( n \) and \( l \)
The azimuthal quantum number \( l \) can take on values from \( 0 \) to \( n-1 \). This means that for a given principal quantum number \( n \), the possible values of \( l \) are:
\[ l = 0, 1, 2, \ldots, (n-1) \]

### Step 2: Calculate the maximum value of \( l \) for \( n = 4 \)
Given \( n = 4 \):
\[ l \text{ can take values from } 0 \text{ to } n-1 = 4-1 = 3 \]
Thus, the possible values of \( l \) are:
\[ l = 0, 1, 2, 3 \]

### Step 3: Identify the options provided
We need to check the options provided in the question to see which one exceeds the maximum value of \( l \) calculated in Step 2. The options are:
1. \( l = 1 \)
2. \( l = 2 \)
3. \( l = 3 \)
4. \( l = 4 \)

### Step 4: Determine which value of \( l \) is not possible
From the possible values of \( l \) (0, 1, 2, 3), we can see that:
- \( l = 1 \) is possible
- \( l = 2 \) is possible
- \( l = 3 \) is possible
- \( l = 4 \) is **not possible** because it exceeds the maximum value of 3.

### Conclusion
The value of \( l \) that is not possible for \( n = 4 \) is:
\[ \text{Option 4: } l = 4 \]