What are the possible values of `m_(l)` for an electron with `l=2` ?

Answer

To determine the possible values of the magnetic quantum number \( m_l \) for an electron with \( l = 2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The azimuthal quantum number \( l \) determines the shape of the orbital and can take on integer values starting from 0 up to \( n-1 \), where \( n \) is the principal quantum number.
- The magnetic quantum number \( m_l \) describes the orientation of the orbital in space.

2. **Determine the Range of \( m_l \)**:
- The magnetic quantum number \( m_l \) can take values ranging from \( -l \) to \( +l \).
- This means that for a given \( l \), the possible values of \( m_l \) are:
\[ m_l = -l, -l + 1, \ldots, 0, \ldots, l - 1, l \]

3. **Substituting the Value of \( l \)**:
- Given \( l = 2 \), we substitute this value into the range for \( m_l \):
\[ m_l = -2, -1, 0, +1, +2 \]

4. **List the Possible Values**:
- Therefore, the possible values of \( m_l \) when \( l = 2 \) are:
\[ m_l = -2, -1, 0, +1, +2 \]

5. **Count the Values**:
- There are a total of 5 possible values for \( m_l \) when \( l = 2 \).

### Final Answer:
The possible values of \( m_l \) for an electron with \( l = 2 \) are:
\[ -2, -1, 0, +1, +2 \]