Which of the following element's outermost orbit's last electron has magnetic quantum number `m = 0`?

Options

A. Na
B. O
C. Cl
D. N

Explanation

To determine which element's outermost orbital's last electron has a magnetic quantum number \( m = 0 \), we need to analyze the electronic configurations of the given elements and identify the last electron added to the outermost orbital.

### Step-by-Step Solution:

1. **Identify the Elements and Their Electronic Configurations**:
- Sodium (Na): The electronic configuration is \( 1s^2 2s^2 2p^6 3s^1 \).
- Oxygen (O): The electronic configuration is \( 1s^2 2s^2 2p^4 \).
- Chlorine (Cl): The electronic configuration is \( 1s^2 2s^2 2p^6 3s^2 3p^5 \).
- Nitrogen (N): The electronic configuration is \( 1s^2 2s^2 2p^3 \).

2. **Determine the Outermost Electron Configuration**:
- For Sodium (Na), the outermost electron is in the \( 3s \) orbital.
- For Oxygen (O), the outermost electrons are in the \( 2s \) and \( 2p \) orbitals.
- For Chlorine (Cl), the outermost electrons are in the \( 3s \) and \( 3p \) orbitals.
- For Nitrogen (N), the outermost electrons are in the \( 2s \) and \( 2p \) orbitals.

3. **Identify the Last Electron and Its Quantum Numbers**:
- For Sodium (Na): The last electron enters the \( 3s \) orbital.
- Principal quantum number \( n = 3 \)
- Azimuthal quantum number \( l = 0 \) (for s orbital)
- Magnetic quantum number \( m = 0 \) (since \( m \) can range from \(-l\) to \(+l\), and \( l = 0 \) gives \( m = 0 \)).

- For Oxygen (O): The last electron enters the \( 2p \) orbital.
- Principal quantum number \( n = 2 \)
- Azimuthal quantum number \( l = 1 \) (for p orbital)
- Possible \( m \) values are \(-1, 0, +1\) (but the last electron in \( 2p^4 \) does not correspond to \( m = 0\)).

- For Chlorine (Cl): The last electron enters the \( 3p \) orbital.
- Principal quantum number \( n = 3 \)
- Azimuthal quantum number \( l = 1 \) (for p orbital)
- Possible \( m \) values are \(-1, 0, +1\) (but the last electron in \( 3p^5 \) does not correspond to \( m = 0\)).

- For Nitrogen (N): The last electron enters the \( 2p \) orbital.
- Principal quantum number \( n = 2 \)
- Azimuthal quantum number \( l = 1 \) (for p orbital)
- Possible \( m \) values are \(-1, 0, +1\) (but the last electron in \( 2p^3 \) does not correspond to \( m = 0\)).

4. **Conclusion**:
- The only element whose outermost orbital's last electron has a magnetic quantum number \( m = 0 \) is Sodium (Na).

### Final Answer:
**Sodium (Na)** is the element whose outermost orbital's last electron has a magnetic quantum number \( m = 0 \).