In the ground state, an element has `13` electrons in its `M` shell. The element is

Options

A. Manganese
B. Cobalt
C. Nickel
D. Iron

Answer

To determine the element that has 13 electrons in its M shell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Electron Shells**:
- The electron shells are designated as K, L, M, etc.
- The K shell (n=1) can hold a maximum of 2 electrons.
- The L shell (n=2) can hold a maximum of 8 electrons.
- The M shell (n=3) can hold a maximum of 18 electrons.

2. **Identify the Total Number of Electrons**:
- The question states that the element has 13 electrons in its M shell.

3. **Determine the Configuration of Electrons**:
- The M shell consists of the 3s, 3p, and 3d subshells.
- To find the total number of electrons in the M shell, we need to add the electrons in these subshells.

4. **Calculate the Electrons in the M Shell**:
- The M shell can be filled as follows:
- 3s can hold 2 electrons.
- 3p can hold 6 electrons.
- 3d can hold up to 10 electrons.
- Therefore, the total number of electrons in the M shell can be calculated as:
\[ \text{Total in M shell} = \text{Electrons in 3s} + \text{Electrons in 3p} + \text{Electrons in 3d} \]
- If we denote the number of electrons in the 3d subshell as \( x \), we can set up the equation:
\[ 2 + 6 + x = 13 \]
- Solving for \( x \):
\[ x = 13 - 8 = 5 \]
- This means there are 5 electrons in the 3d subshell.

5. **Identify the Element**:
- The total number of electrons in the atom is the sum of the electrons in all shells.
- The K shell has 2 electrons, the L shell has 8 electrons, and the M shell has 13 electrons.
- Therefore, the total number of electrons is:
\[ 2 + 8 + 13 = 23 \]
- The atomic number of the element is 23, which corresponds to the element Vanadium (V).

### Conclusion:
The element with 13 electrons in its M shell is **Vanadium (V)**.