Maximum numbe of electron in a subshell is given by

Options

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

Answer

To determine the maximum number of electrons in a subshell, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (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 in the Subshell**:
- The number of orbitals in a subshell is given by the formula:
\[ \text{Number of orbitals} = 2l + 1 \]
- This formula accounts for the different orientations of the orbitals within a subshell.

3. **Determine the Maximum Number of Electrons**:
- Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle).
- Therefore, to find the maximum number of electrons in a subshell, we multiply the number of orbitals by the maximum number of electrons per orbital:
\[ \text{Maximum number of electrons} = (\text{Number of orbitals}) \times 2 = (2l + 1) \times 2 \]
- Simplifying this gives:
\[ \text{Maximum number of electrons} = 4l + 2 \]
- Alternatively, this can also be expressed as:
\[ \text{Maximum number of electrons} = 2(2l + 1) \]

4. **Conclusion**:
- Thus, the maximum number of electrons in a subshell is given by:
\[ \text{Maximum number of electrons} = 2(2l + 1) \]

### Final Answer:
The maximum number of electrons in a subshell is given by \( 2(2l + 1) \).

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