Which set is expected to show the smallest difference in `IE_(1)` ?

Options

A. `He,Ne,Ar`
B. `B,N,O`
C. `Mg,Mg^(o+),Mg^(+2)`
D. `Fe,CO,Ni`

Explanation

To determine which set is expected to show the smallest difference in first ionization energy (IE₁), we will analyze the provided options based on the trends in ionization energy across periods and groups in the periodic table.

### Step-by-Step Solution:

1. **Understanding Ionization Energy (IE)**:
- Ionization energy is the energy required to remove the outermost electron from a neutral atom.
- Generally, ionization energy increases across a period (left to right) and decreases down a group (top to bottom).

2. **Analyzing the Given Sets**:
- We have four sets to analyze:
- Set A: Helium (He), Neon (Ne), Argon (Ar)
- Set B: Boron (B), Nitrogen (N), Oxygen (O)
- Set C: Magnesium ion (Mg⁺), Magnesium ion (Mg²⁺)
- Set D: Iron (Fe), Cobalt (Co), Nickel (Ni)

3. **Set A: Helium, Neon, Argon**:
- All three elements are noble gases. They have very high ionization energies and are stable due to their full valence shells. However, the difference in their ionization energies is significant due to their atomic size and position in the periodic table.

4. **Set B: Boron, Nitrogen, Oxygen**:
- These elements are in the same period. As we move from Boron to Oxygen, the ionization energy increases due to increasing nuclear charge and decreasing atomic radius. Thus, there will be a noticeable difference in their ionization energies.

5. **Set C: Mg⁺, Mg²⁺**:
- This set involves ionized forms of magnesium. The first ionization energy (Mg to Mg⁺) and the second ionization energy (Mg⁺ to Mg²⁺) are significantly different because removing an electron from a stable noble gas configuration (after the first ionization) requires much more energy. Therefore, this set will show a large difference in ionization energy.

6. **Set D: Iron, Cobalt, Nickel**:
- These elements are transition metals and belong to the d-block of the periodic table. They have similar electron configurations and thus have relatively small differences in their ionization energies.

7. **Conclusion**:
- Among the given sets, Set D (Iron, Cobalt, Nickel) is expected to show the smallest difference in first ionization energy because they are all transition metals with similar electronic configurations.

### Final Answer:
The set expected to show the smallest difference in IE₁ is **Set D: Iron (Fe), Cobalt (Co), Nickel (Ni)**.