The maximum number of electrons in a subshell is given by the expression

Options

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

Explanation

To determine the maximum number of electrons in a subshell, we can use the following steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- Each electron in an atom is described by a set of four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).
- The azimuthal quantum number (l) defines the shape of the subshell and can take values from 0 to (n-1).

2. **Maximum Electrons in a Subshell**:
- The maximum number of electrons that can occupy a subshell is determined by the azimuthal quantum number (l).
- For a given value of l, the number of possible values for the magnetic quantum number (m_l) is given by the range from -l to +l, which gives a total of (2l + 1) possible values.

3. **Considering Spin**:
- Each orbital can hold a maximum of 2 electrons (due to the two possible spin states: +1/2 and -1/2).
- Therefore, the total maximum number of electrons in a subshell can be calculated as:
\[ \text{Maximum electrons} = 2 \times (2l + 1) = 4l + 2 \]

4. **Identifying the Correct Expression**:
- The expression for the maximum number of electrons in a subshell is thus \(4l + 2\).
- This can also be expressed in the form \(2(2l + 1)\), which simplifies to \(2n^2\) for the maximum number of electrons in a shell.

5. **Conclusion**:
- From the options provided, the correct expression for the maximum number of electrons in a subshell is \(4l + 2\).

### Final Answer:
The maximum number of electrons in a subshell is given by the expression \(4l + 2\).

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