Which of the following order of radii is correct?

Options

A. Li < Be < Mg
B. `O^(+) lt O^(2-) lt N^(3-)`
C. `O lt F lt Ne`
D. `Na^(+) gt F^(-) gt O^(2-)`

Explanation

To determine the correct order of atomic radii from the given options, we need to analyze the trends in atomic size based on periodic properties. Let's break down the solution step by step.

### Step 1: Understand Atomic Radius Trends
- Atomic radius generally increases down a group in the periodic table due to the addition of electron shells.
- Atomic radius generally decreases across a period from left to right due to an increase in effective nuclear charge, which pulls the electrons closer to the nucleus.

**Hint:** Remember the trends: size increases down a group and decreases across a period.

### Step 2: Analyze the First Set (Li, Be, Mg)
- Lithium (Li) is in Group 1, Beryllium (Be) is in Group 2, and Magnesium (Mg) is in Group 2 but below Be.
- As we move down from Li to Mg, the atomic radius increases. However, Be, being to the right of Li, will have a smaller radius than Li.
- Therefore, the order should be: **Mg > Li > Be**.

**Hint:** Compare the positions of the elements in the periodic table to determine their sizes.

### Step 3: Analyze the Second Set (O²⁻, O, N³⁻)
- O²⁻ (oxide ion) has gained two electrons, leading to increased electron-electron repulsion, resulting in a larger radius.
- O (neutral oxygen) has a smaller radius than O²⁻.
- N³⁻ (nitride ion) has gained three electrons, leading to even more electron-electron repulsion than O²⁻, making it the largest.
- Therefore, the order should be: **N³⁻ > O²⁻ > O**.

**Hint:** Remember that anions are larger than their neutral atoms due to added electrons and increased repulsion.

### Step 4: Analyze the Third Set (O, F, Ne)
- Oxygen (O) is to the left of Fluorine (F), and Fluorine is to the left of Neon (Ne).
- As we move from O to Ne, the atomic radius decreases.
- Therefore, the order should be: **O > F > Ne**.

**Hint:** Use the left-to-right trend in a period to compare sizes.

### Step 5: Analyze the Fourth Set (Cations vs. Anions)
- Cations (positively charged ions) are smaller than their neutral atoms due to the loss of electrons and reduced electron-electron repulsion.
- Anions (negatively charged ions) are larger than their neutral atoms due to the gain of electrons and increased electron-electron repulsion.
- Therefore, the order should be: **Cations < Neutral Atoms < Anions**.

**Hint:** Remember that cations are smaller than their neutral counterparts, while anions are larger.

### Conclusion
After analyzing all sets, we find that the correct order of radii is:
1. For the first set: **Mg > Li > Be** (incorrect order given)
2. For the second set: **N³⁻ > O²⁻ > O** (correct order)
3. For the third set: **O > F > Ne** (correct order)
4. For the fourth set: **Cations < Neutral < Anions** (correct order)

Thus, the correct answer is the second set, where the order of radii is **N³⁻ > O²⁻ > O**.