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

Options

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

Explanation

To determine which set of elements is expected to show the smallest difference in first ionization energy (IE₁), we need to analyze the options provided based on the trends in ionization energy in the periodic table.

### Step-by-Step Solution:

1. **Understanding Ionization Energy (IE)**:
- Ionization energy is the amount of energy required to remove an electron from an isolated gaseous atom.
- Generally, ionization energy increases across a period and decreases down a group.

2. **Analyzing the First Option: Helium, Neon, and Argon**:
- These elements are noble gases located in Group 18.
- As we move down the group from Helium to Argon, the ionization energy decreases due to increased atomic size and electron shielding.
- The difference in ionization energy between these noble gases is significant because they have very high ionization energies.
- **Conclusion**: This option is not expected to show the smallest difference in IE₁.

3. **Analyzing the Second Option: Magnesium, Mg⁺, and Mg²⁺**:
- Here we are looking at the ionization energies of the same element in different ionization states.
- The first ionization energy (IE₁) is for removing one electron from neutral magnesium, while the second ionization energy (IE₂) is for removing an electron from a singly charged magnesium ion (Mg⁺).
- The second ionization energy is significantly higher than the first because removing an electron from a positively charged ion requires much more energy due to increased effective nuclear charge.
- **Conclusion**: This option is not expected to show the smallest difference in IE₁.

4. **Analyzing the Third Option: Boron, Nitrogen, and Oxygen**:
- These elements are in the same period (Period 2) and show increasing ionization energy from Boron to Oxygen.
- The differences in their ionization energies are significant since nitrogen and oxygen have higher electronegativities than boron.
- **Conclusion**: This option is not expected to show the smallest difference in IE₁.

5. **Analyzing the Fourth Option: Iron, Cobalt, and Nickel**:
- These elements are transition metals and are in the same series (3d series).
- As we move from Iron to Nickel, the addition of d-electrons leads to increased shielding and a gradual increase in ionization energy.
- The differences in ionization energies among these transition metals are relatively small compared to the other options due to similar electron configurations and shielding effects.
- **Conclusion**: This option is expected to show the smallest difference in IE₁.

### Final Answer:
The set that is expected to show the smallest difference in first ionization energy (IE₁) is **Iron, Cobalt, and Nickel**.

---