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 quantum numbers \( n = 3 \) and \( l = 3 \), 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 \( l \) indicates the subshell type. The value of \( l \) can range from \( 0 \) to \( n-1 \).

### Step 2: Determine Possible Values of \( l \)
For \( n = 3 \):
- The possible values of \( l \) are:
- \( l = 0 \) (s subshell)
- \( l = 1 \) (p subshell)
- \( l = 2 \) (d subshell)

This means that the maximum value of \( l \) when \( n = 3 \) is \( 2 \).

### Step 3: Analyze the Given Value of \( l \)
The question specifies \( l = 3 \). However, since the maximum value of \( l \) for \( n = 3 \) is \( 2 \), \( l = 3 \) is not a valid state for this energy level.

### Step 4: Conclusion on Electron Count
Since \( l = 3 \) does not exist when \( n = 3 \), there cannot be any electrons in this state. 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**.

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