The total number of electrons in a subshell designated by azimuthal quantum number, l is given as

Options

A. `2l+l`
B. `l^(2)`
C. `4l+2`
D. `2l+2`

Explanation

To find the total number of electrons in a subshell designated by the azimuthal quantum number \( l \), we can use the following steps:

### Step 1: Understand the Quantum Numbers
The azimuthal quantum number \( l \) determines the shape of the orbital and can take values from \( 0 \) to \( n-1 \), where \( n \) is the principal quantum number. Each value of \( l \) corresponds to a specific subshell:
- \( l = 0 \) corresponds to the s subshell
- \( l = 1 \) corresponds to the p subshell
- \( l = 2 \) corresponds to the d subshell
- \( l = 3 \) corresponds to the f subshell

### Step 2: Use the Formula
The total number of electrons that can occupy a subshell is given by the formula:
\[ \text{Total Electrons} = 4l + 2 \]
This formula accounts for the maximum number of electrons that can fit into the orbitals of a given subshell.

### Step 3: Apply the Formula
To find the total number of electrons in a subshell, substitute the value of \( l \) into the formula. For example:
- If \( l = 0 \) (s subshell):
\[ \text{Total Electrons} = 4(0) + 2 = 2 \]
- If \( l = 1 \) (p subshell):
\[ \text{Total Electrons} = 4(1) + 2 = 6 \]
- If \( l = 2 \) (d subshell):
\[ \text{Total Electrons} = 4(2) + 2 = 10 \]
- If \( l = 3 \) (f subshell):
\[ \text{Total Electrons} = 4(3) + 2 = 14 \]

### Conclusion
Thus, the total number of electrons in a subshell designated by the azimuthal quantum number \( l \) is given by the formula \( 4l + 2 \).

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