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 (which has an atomic number of 26) in its \( M^{3+} \) state, we can follow these steps:

### Step 1: Identify the Element
The atomic number of 26 corresponds to the element Iron (Fe).

### Step 2: Write the Electron Configuration
For a neutral iron atom (atomic number 26), the electron configuration is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^6 \]

### Step 3: Determine the Oxidation State
In the \( M^{3+} \) state, iron loses three electrons. The removal of electrons typically occurs from the outermost shell first, which includes the 4s and then the 3d subshell.

### Step 4: Remove Electrons for the \( M^{3+} \) State
1. Remove 2 electrons from the 4s subshell.
2. Remove 1 electron from the 3d subshell.

Thus, the electron configuration for \( Fe^{3+} \) becomes:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \]

### Step 5: Identify the M-shell
The M-shell corresponds to the principal quantum number \( n = 3 \). The subshells in the M-shell are:
- 3s
- 3p
- 3d

### Step 6: Count the Electrons in the M-shell
Now, we count the electrons in the M-shell:
- From the 3s subshell: 2 electrons
- From the 3p subshell: 6 electrons
- From the 3d subshell: 5 electrons

Total electrons in the M-shell:
\[ 2 + 6 + 5 = 13 \text{ electrons} \]

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

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