The correct order of radii is

Options

A. `N lt Be lt B`
B. `F^(ɵ)lt O^(2-) lt N^(3-)`
C. `Na lt Li lt K`
D. `Fe^(3+)lt Fe^(2+)lt Fe^(4+)`

Explanation

To determine the correct order of radii for the given elements and ions, we will analyze each group step by step.

### Step 1: Analyzing the first group (Nitrogen, Beryllium, Boron)
1. **Identify the elements**: Nitrogen (N), Beryllium (Be), Boron (B).
2. **Understand the trend in a period**: As we move from left to right in a period, the atomic number increases, leading to an increase in nuclear charge.
3. **Effect on atomic size**: Increased nuclear charge pulls electrons closer to the nucleus, resulting in a decrease in atomic size.
4. **Order of radii**: Therefore, the order of radii from largest to smallest is:
- Be > B > N
- In terms of inequality: N < B < Be.

### Step 2: Analyzing the second group (Anions: N³⁻, O²⁻, F⁻)
1. **Identify the anions**: N³⁻, O²⁻, F⁻.
2. **Understand the effect of charge on size**: More negative charge means less nuclear charge relative to the number of electrons, leading to a larger radius.
3. **Order of radii**: The order based on charge is:
- N³⁻ > O²⁻ > F⁻.

### Step 3: Analyzing the third group (Cations: Li, Na, K)
1. **Identify the elements**: Lithium (Li), Sodium (Na), Potassium (K).
2. **Understand the trend in a group**: As we move down a group, additional electron shells are added, which increases atomic size.
3. **Order of radii**: Therefore, the order of radii from smallest to largest is:
- Li < Na < K.

### Step 4: Analyzing the fourth group (Cations: Fe³⁺, Fe²⁺, Fe⁴⁺)
1. **Identify the cations**: Fe³⁺, Fe²⁺, Fe⁴⁺.
2. **Understand the effect of charge on size**: More positive charge means a stronger attraction between the nucleus and the electrons, resulting in a smaller radius.
3. **Order of radii**: The order based on charge is:
- Fe⁴⁺ < Fe³⁺ < Fe²⁺.

### Final Summary of Orders
1. **First group**: N < B < Be
2. **Second group**: N³⁻ > O²⁻ > F⁻
3. **Third group**: Li < Na < K
4. **Fourth group**: Fe⁴⁺ < Fe³⁺ < Fe²⁺

### Conclusion
The correct order of radii is found in the second option regarding the anions, which is correct.

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