For sodium atom the number of electrons with m=0 will be

Options

A. 2
B. 7
C. 9
D. 8

Explanation

To determine the number of electrons with a magnetic quantum number (m) equal to 0 in a sodium atom, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number of Sodium:**
Sodium (Na) has an atomic number of 11, which means it has 11 electrons.

2. **Write the Electronic Configuration:**
The electronic configuration of sodium is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^1 \]

3. **Understand Quantum Numbers:**
- The principal quantum number (n) indicates the shell level.
- The azimuthal quantum number (l) indicates the subshell:
- For s subshell, \( l = 0 \)
- For p subshell, \( l = 1 \)
- For d subshell, \( l = 2 \)
- For f subshell, \( l = 3 \)
- The magnetic quantum number (m) can take values from \(-l\) to \(+l\).

4. **Determine m for Each Subshell:**
- **For 1s²:**
- \( n = 1 \), \( l = 0 \) (s subshell)
- Possible m values: \( m = 0 \)
- Number of electrons with \( m = 0 \): 2 (both electrons can have \( m = 0 \))

- **For 2s²:**
- \( n = 2 \), \( l = 0 \) (s subshell)
- Possible m values: \( m = 0 \)
- Number of electrons with \( m = 0 \): 2 (both electrons can have \( m = 0 \))

- **For 2p⁶:**
- \( n = 2 \), \( l = 1 \) (p subshell)
- Possible m values: \( m = -1, 0, +1 \)
- Number of electrons with \( m = 0 \): 2 (there are 6 electrons in total, distributed among three m values)

- **For 3s¹:**
- \( n = 3 \), \( l = 0 \) (s subshell)
- Possible m values: \( m = 0 \)
- Number of electrons with \( m = 0 \): 1 (only one electron in this subshell)

5. **Total Count of Electrons with m = 0:**
- From 1s²: 2 electrons
- From 2s²: 2 electrons
- From 2p⁶: 2 electrons
- From 3s¹: 1 electron
- Total = \( 2 + 2 + 2 + 1 = 7 \)

### Final Answer:
The total number of electrons in a sodium atom with \( m = 0 \) is **7**.

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