The element which has half-filled d-orbitals in its `'+1'` oxidation state is

Options

A. Mn
B. Cr
C. Zn
D. Fe

Answer

To determine which element has half-filled d-orbitals in its +1 oxidation state, we will analyze the electron configurations of the given elements: manganese (Mn), chromium (Cr), zinc (Zn), and iron (Fe).

### Step-by-Step Solution:

1. **Identify the Electron Configurations:**
- Manganese (Mn): Atomic number = 25
- Ground state electron configuration: \( [Ar] 3d^5 4s^2 \)
- Chromium (Cr): Atomic number = 24
- Ground state electron configuration: \( [Ar] 3d^5 4s^1 \) (due to stability of half-filled d-orbitals)
- Zinc (Zn): Atomic number = 30
- Ground state electron configuration: \( [Ar] 3d^{10} 4s^2 \)
- Iron (Fe): Atomic number = 26
- Ground state electron configuration: \( [Ar] 3d^6 4s^2 \)

2. **Determine the Electron Configurations in +1 Oxidation State:**
- Manganese (Mn):
- \( Mn^+ \): Remove one electron from 4s orbital
- Configuration: \( [Ar] 3d^5 4s^1 \)
- Chromium (Cr):
- \( Cr^+ \): Remove one electron from 4s orbital
- Configuration: \( [Ar] 3d^5 \)
- Zinc (Zn):
- \( Zn^+ \): Remove one electron from 4s orbital
- Configuration: \( [Ar] 3d^{10} 4s^1 \)
- Iron (Fe):
- \( Fe^+ \): Remove one electron from 4s orbital
- Configuration: \( [Ar] 3d^6 4s^1 \)

3. **Analyze the Half-Filled d-Orbitals:**
- Manganese (Mn): \( 3d^5 4s^1 \) - 5 electrons in 3d (half-filled)
- Chromium (Cr): \( 3d^5 \) - 5 electrons in 3d (half-filled)
- Zinc (Zn): \( 3d^{10} 4s^1 \) - 10 electrons in 3d (not half-filled)
- Iron (Fe): \( 3d^6 4s^1 \) - 6 electrons in 3d (not half-filled)

4. **Conclusion:**
- The only element with half-filled d-orbitals in its +1 oxidation state is **Chromium (Cr)**, as it has a configuration of \( 3d^5 \) in this state.

### Final Answer:
The element which has half-filled d-orbitals in its +1 oxidation state is **Chromium (Cr)**.