For azimuthal quantum number l=3, the maximum number of electrons will be

Options

A. 2
B. 6
C. 0
D. 14

Explanation

To determine the maximum number of electrons that can be accommodated for an azimuthal quantum number \( l = 3 \), we can follow these steps:

### Step 1: Understand the relationship between azimuthal quantum number and magnetic quantum number
The azimuthal quantum number \( l \) defines the shape of the orbital and can take on integer values from 0 to \( n-1 \), where \( n \) is the principal quantum number. The maximum number of orbitals for a given \( l \) can be calculated using the formula for the magnetic quantum number \( m \).

### Step 2: Calculate the number of orbitals
The formula for the magnetic quantum number \( m \) is given by:
\[ m = -l, -l + 1, ..., 0, ..., l - 1, l \]
This means the total number of possible \( m \) values is:
\[ 2l + 1 \]
For \( l = 3 \):
\[ m = 2(3) + 1 = 7 \]
So, there are 7 orbitals when \( l = 3 \).

### Step 3: Determine the maximum number of electrons
Each orbital can hold a maximum of 2 electrons. Therefore, the total number of electrons that can be accommodated in these orbitals is:
\[ \text{Total electrons} = \text{Number of orbitals} \times 2 \]
Substituting the number of orbitals we found:
\[ \text{Total electrons} = 7 \times 2 = 14 \]

### Conclusion
Thus, the maximum number of electrons that can be accommodated for \( l = 3 \) is **14**.

### Final Answer
The correct answer is option 4: **14**.

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