Maximum number of electrons in a sub-shell of an atom is determined by the following.

Options

A. 4l +2
B. 2l +1
C. 4l -2
D. `2n^(2)`

Explanation

To determine the maximum number of electrons in a sub-shell of an atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Number (l)**:
- The angular momentum quantum number, denoted as \( l \), defines the shape of the orbital and can take values from 0 to \( n-1 \), where \( n \) is the principal quantum number.

2. **Calculate the Number of Orbitals**:
- The number of orbitals in a sub-shell is given by the formula:
\[ \text{Number of orbitals} = 2l + 1 \]
- This formula accounts for the different orientations of the orbitals within a sub-shell.

3. **Determine Maximum Electrons per Orbital**:
- Each orbital can hold a maximum of 2 electrons due to the Pauli exclusion principle.

4. **Calculate Maximum Number of Electrons in the Sub-shell**:
- To find the maximum number of electrons in a sub-shell, multiply the number of orbitals by the maximum number of electrons per orbital:
\[ \text{Maximum electrons} = 2 \times (\text{Number of orbitals}) = 2 \times (2l + 1) \]
- Simplifying this gives:
\[ \text{Maximum electrons} = 4l + 2 \]

5. **Final Formula**:
- Therefore, the formula to calculate the maximum number of electrons in a sub-shell is:
\[ \text{Maximum electrons} = 4l + 2 \]

### Conclusion:
The maximum number of electrons in a sub-shell is determined by the formula \( 4l + 2 \).