1. We compare the stability of nitrogen trihalides $NX_3$ where $X=F,Cl,Br,I$.

2. Key factor: bond strength of the $N-X$ bond

   • Stability of $NX_3$ depends largely on how strong the $N-X$ bonds are.
   • Because nitrogen is very small, it forms the strongest bond with the smallest halogen, fluorine.
   • As we move down the group: $N-F > N-Cl > N-Br > N-I$ in bond strength.

3. Effect of size mismatch and repulsion

   • In $NCl_3$, $NBr_3$, and especially $NI_3$, the larger halogen atoms lead to poorer overlap with nitrogen orbitals.
   • This makes the bonds weaker and the compounds less stable.
   • $NI_3$ is extremely unstable and explosive.

4. Why $NF_3$ is most stable

   • $N-F$ bond is strongest due to effective orbital overlap.
   • Although fluorine is highly electronegative, $NF_3$ is a well-known stable compound.
   • Thus among all nitrogen trihalides, $NF_3$ is the most stable.

5. Option-wise check

   • A: $NF_3$ — most stable ✅
   • B: $NCl_3$ — less stable than $NF_3$
   • C: $NBr_3$ — even less stable
   • D: $NI_3$ — least stable, highly explosive

Therefore, the most stable trihalide of nitrogen is: $\boxed{NF_3}$