The maximum number of electrons possible in subshell is equal to

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The azimuthal quantum number (l) defines the shape of the orbital and the type of subshell. The values of l can be 0 (s subshell), 1 (p subshell), 2 (d subshell), and 3 (f subshell).

2. **Determine the Number of Orbitals**:
- The number of orbitals in a subshell is given by the formula \(2l + 1\). This accounts for the different orientations of the orbitals.

3. **Calculate the Maximum Number of Electrons**:
- Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle, where two electrons can occupy the same orbital only if they have opposite spins).
- Therefore, the total maximum number of electrons in a subshell can be calculated using the formula:
\[ \text{Maximum Electrons} = 2 \times (\text{Number of Orbitals}) = 2 \times (2l + 1) \]

4. **Simplify the Formula**:
- By simplifying the above expression, we get:
\[ \text{Maximum Electrons} = 2(2l + 1) = 4l + 2 \]

5. **Conclusion**:
- Thus, the maximum number of electrons possible in a subshell is given by the formula \(4l + 2\).

### Final Answer:
The maximum number of electrons possible in a subshell is **4l + 2**.

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