The correct order of radii is:

Options

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

Explanation

To solve the question regarding the correct order of atomic radii, we will analyze the given options step by step.

### Step 1: Analyze the first option (N, Be, B)
- **Elements**: Nitrogen (N), Beryllium (Be), Boron (B)
- **Period**: All three elements are in the same period (Period 2).
- **Trend**: Atomic radius decreases from left to right across a period due to increasing nuclear charge.
- **Conclusion**: The order should be Be > B > N. Therefore, this option is incorrect.

### Step 2: Analyze the second option (F, O, N)
- **Species**: F, O, N are isoelectronic species (F^-, O^2-, N^3-).
- **Electrons**: All have 10 electrons.
- **Trend**: As the negative charge increases, the size of the anion increases due to electron-electron repulsion.
- **Conclusion**: The order should be N^3- > O^2- > F^- (largest to smallest). Therefore, this option is correct.

### Step 3: Analyze the third option (Na, Li, K)
- **Elements**: Sodium (Na), Lithium (Li), Potassium (K)
- **Group**: All three elements are in the same group (Group 1).
- **Trend**: Atomic radius increases down a group due to the addition of electron shells.
- **Conclusion**: The correct order should be Li < Na < K (smallest to largest). Therefore, this option is incorrect.

### Step 4: Analyze the fourth option (Fe^3+, Fe^2+, Fe^4+)
- **Ions**: Fe^3+, Fe^2+, Fe^4+
- **Trend**: For the same element, as the positive charge increases, the size decreases due to greater nuclear attraction on the remaining electrons.
- **Conclusion**: The correct order should be Fe^4+ < Fe^3+ < Fe^2+ (smallest to largest). Therefore, this option is incorrect.

### Final Conclusion
The only correct order of radii is from the second option: F, O, N (isoelectronic species) with the order being N^3- > O^2- > F^-.