The maximum number of electrons with n = 3 and I = 3 is

Options

A. 11
B. 6
C. 10
D. 0

Answer

To solve the question regarding the maximum number of electrons with principal quantum number \( n = 3 \) and azimuthal quantum number \( l = 3 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
The principal quantum number \( n \) indicates the energy level of an electron in an atom, while the azimuthal quantum number \( l \) defines the shape of the orbital. The value of \( l \) can range from \( 0 \) to \( n-1 \).

### Step 2: Determine Possible Values of \( l \)
For a given \( n \):
- The possible values of \( l \) are \( 0, 1, 2, \ldots, n-1 \).
- Therefore, for \( n = 3 \), the possible values of \( l \) are:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbital)
- \( l = 2 \) (d orbital)

### Step 3: Analyze the Given \( l \)
In the question, we have \( l = 3 \). However, according to the rules of quantum mechanics:
- The maximum value of \( l \) for \( n = 3 \) is \( n-1 = 2 \).
- This means \( l = 3 \) is not a valid azimuthal quantum number for \( n = 3 \).

### Step 4: Conclusion
Since \( l = 3 \) is not a valid quantum number for \( n = 3 \), there cannot be any electrons associated with this configuration. Therefore, the maximum number of electrons with \( n = 3 \) and \( l = 3 \) is **0**.

### Final Answer
The maximum number of electrons with \( n = 3 \) and \( l = 3 \) is **0**.