The atomic number of an element M is 26. How many electrons are present in the M-shell of the element in its `M^(3+)` state

Options

A. 11
B. 15
C. 14
D. 13

Explanation

To determine the number of electrons present in the M-shell of the element M with atomic number 26 in its \( M^{3+} \) state, follow these steps:

### Step 1: Determine the Electronic Configuration
The atomic number of the element M is 26. The electronic configuration for an element with atomic number 26 (iron, Fe) is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^6 \]

### Step 2: Identify the State of the Element
The element is in the \( M^{3+} \) state, which means it has lost 3 electrons. We need to remove these electrons from the outermost shells first.

### Step 3: Remove Electrons for the \( M^{3+} \) State
When removing electrons, we first remove from the 4s and then from the 3d subshell:
- Remove 2 electrons from the 4s subshell: \( 4s^2 \) becomes \( 4s^0 \)
- Remove 1 electron from the 3d subshell: \( 3d^6 \) becomes \( 3d^5 \)

Thus, the electronic configuration in the \( M^{3+} \) state is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \]

### Step 4: Identify the Electrons in the M-shell
The M-shell corresponds to the principal quantum number \( n = 3 \). The electrons in the M-shell are from the 3s, 3p, and 3d subshells:
- From 3s: 2 electrons
- From 3p: 6 electrons
- From 3d: 5 electrons

### Step 5: Calculate the Total Electrons in the M-shell
Now, add the electrons from the 3s, 3p, and 3d subshells:
\[ 2 \, (from \, 3s) + 6 \, (from \, 3p) + 5 \, (from \, 3d) = 13 \, electrons \]

### Conclusion
Therefore, the total number of electrons present in the M-shell of the element M in its \( M^{3+} \) state is **13**.

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