How many electrons in Argon have `m = 0` ?

Options

A. 12
B. 10
C. 8
D. 6

Explanation

To determine how many electrons in Argon have a magnetic quantum number (m) equal to 0, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number of Argon**:
- Argon has an atomic number of 18, which means it has 18 electrons.

2. **Write the Electron Configuration**:
- The electron configuration of Argon is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \]

3. **Determine the Contribution from Each Subshell**:
- **1s Subshell**:
- The azimuthal quantum number (l) for the s subshell is 0.
- The magnetic quantum number (m) can only be 0.
- Therefore, from the 1s subshell, there are **2 electrons** with m = 0.

- **2s Subshell**:
- Again, for the s subshell, l = 0 and m = 0.
- Thus, from the 2s subshell, there are **2 electrons** with m = 0.

- **2p Subshell**:
- For the p subshell, l = 1, and m can be -1, 0, or +1.
- There are 3 orbitals (px, py, pz), and each can hold 2 electrons.
- Therefore, from the 2p subshell, there is **1 electron** with m = 0 (it can be in any of the three orbitals).

- **3s Subshell**:
- Similar to the previous s subshells, l = 0 and m = 0.
- Thus, from the 3s subshell, there are **2 electrons** with m = 0.

- **3p Subshell**:
- For the p subshell, l = 1 and m can be -1, 0, or +1.
- Again, there are 3 orbitals, and thus there is **1 electron** with m = 0.

4. **Add All Contributions**:
- Now, we sum up the contributions:
- From 1s: 2 electrons
- From 2s: 2 electrons
- From 2p: 1 electron
- From 3s: 2 electrons
- From 3p: 1 electron
- Total = \(2 + 2 + 1 + 2 + 1 = 8\) electrons.

### Final Answer:
- Therefore, the total number of electrons in Argon that have \( m = 0 \) is **8**.

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