In an atom which has 2K, 8L , 18 M and 2N electrons in the ground state . The total number of electrons having magnetic quantum number m=0 is

Options

A. 6
B. 10
C. 7
D. 14

Answer

To solve the problem, we need to determine the total number of electrons in an atom that have a magnetic quantum number (m) equal to zero. We are given the distribution of electrons in the shells K, L, M, and N as follows: 2 in K, 8 in L, 18 in M, and 2 in N.

### Step-by-Step Solution:

1. **Identify the Electron Configuration**:
- The atom has:
- K shell: 2 electrons (1s²)
- L shell: 8 electrons (2s² 2p⁶)
- M shell: 18 electrons (3s² 3p⁶ 3d¹⁰)
- N shell: 2 electrons (4s²)
- Therefore, the total electron configuration can be written as:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s²

2. **Count the Electrons in Each Subshell**:
- For each subshell, we identify how many electrons have m = 0:
- **1s²**: 2 electrons (m = 0)
- **2s²**: 2 electrons (m = 0)
- **2p⁶**: 2 electrons (m = -1, 0, +1; m = 0 has 2 electrons)
- **3s²**: 2 electrons (m = 0)
- **3p⁶**: 2 electrons (m = -1, 0, +1; m = 0 has 2 electrons)
- **3d¹⁰**: 2 electrons (m = -2, -1, 0, +1, +2; m = 0 has 2 electrons)
- **4s²**: 2 electrons (m = 0)

3. **Total the Electrons with m = 0**:
- Now we sum the electrons with m = 0 from each subshell:
- 1s: 2
- 2s: 2
- 2p: 2
- 3s: 2
- 3p: 2
- 3d: 2
- 4s: 2
- Total = 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14

4. **Final Answer**:
- The total number of electrons having a magnetic quantum number m = 0 is **14**.