Maximum number of electrons in a sub-shell with `l = 3` and `n = 4` is.

Options

A. 10
B. 12
C. 14
D. 16

Explanation

To determine the maximum number of electrons in a sub-shell with \( l = 3 \) and \( n = 4 \), we can follow these steps:

### Step 1: Identify the sub-shell
The quantum number \( l \) represents the angular momentum quantum number, which determines the shape of the orbital. The values of \( l \) correspond to different types of orbitals:
- \( l = 0 \) corresponds to s-orbitals
- \( l = 1 \) corresponds to p-orbitals
- \( l = 2 \) corresponds to d-orbitals
- \( l = 3 \) corresponds to f-orbitals

Since \( l = 3 \), we are dealing with an f-orbital.

### Step 2: Determine the principal quantum number
The principal quantum number \( n \) indicates the energy level of the electron. In this case, \( n = 4 \) means we are looking at the 4f sub-shell.

### Step 3: Calculate the maximum number of electrons
The maximum number of electrons in a sub-shell can be calculated using the formula:
\[ \text{Maximum number of electrons} = 2(2l + 1) \]
Substituting \( l = 3 \):
\[ \text{Maximum number of electrons} = 2(2 \times 3 + 1) = 2(6 + 1) = 2 \times 7 = 14 \]

### Conclusion
Thus, the maximum number of electrons in the sub-shell with \( l = 3 \) and \( n = 4 \) is **14 electrons**.

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