Step 1: Understanding the Question:
The question asks for the reactivity trend of different alkyl halides in nucleophilic substitution reactions (specifically with ammonia).
Step 2: Detailed Explanation:
1. The reaction with ammonia is an ammonolysis reaction, which is a type of nucleophilic substitution.
2. Reactivity of alkyl halides depends on the strength of the $C-X$ bond.
3. Bond strength decreases as the size of the halogen atom increases down the group ($Cl<Br<I$).
4. The $C-I$ bond is the longest and weakest, making it the easiest to break. The $C-Cl$ bond is the shortest and strongest.
5. Therefore, alkyl iodides are the most reactive and alkyl chlorides are the least reactive.
Step 4: Final Answer:
The correct order of reactivity is $R-I>R-Br>R-Cl$.