The atomic number of an element 'M' is 26. How many electrons are present in the M-shell of the element in its `M^(2+)` state ?

Options

A. 5
B. 14
C. 12
D. 13

Answer

To find the number of electrons present in the M-shell of the element 'M' (which has an atomic number of 26, corresponding to iron, Fe) in its \( \text{Fe}^{2+} \) state, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Atomic Number**:
The atomic number of the element \( M \) is given as 26. This means the element is iron (Fe).

2. **Write the Electronic Configuration of Fe**:
The electronic configuration of iron (Fe) can be written as:
\[ \text{Fe: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^6 \]
This can also be represented using the noble gas configuration:
\[ \text{Fe: } [\text{Ar}] \, 4s^2 \, 3d^6 \]

3. **Determine the Electronic Configuration of \( \text{Fe}^{2+} \)**:
When iron loses two electrons to form \( \text{Fe}^{2+} \), the electrons are removed first from the 4s orbital. Thus, the electronic configuration of \( \text{Fe}^{2+} \) is:
\[ \text{Fe}^{2+}: [\text{Ar}] \, 3d^6 \]

4. **Identify the Shells**:
- The K-shell corresponds to \( n=1 \) (2 electrons).
- The L-shell corresponds to \( n=2 \) (8 electrons).
- The M-shell corresponds to \( n=3 \) (which can hold up to 18 electrons).

5. **Count the Electrons in the M-shell**:
In the case of \( \text{Fe}^{2+} \), the electrons in the M-shell (3s and 3p orbitals) are:
- From the 3s orbital: 2 electrons
- From the 3p orbital: 6 electrons
- From the 3d orbital: 6 electrons

Therefore, the total number of electrons in the M-shell is:
\[ 2 \, (\text{from } 3s) + 6 \, (\text{from } 3p) + 6 \, (\text{from } 3d) = 14 \text{ electrons} \]

### Final Answer:
The number of electrons present in the M-shell of the element \( M \) in its \( \text{Fe}^{2+} \) state is **14**.

---