Read the passage carefully and answer the Questions
The decomposition of \(N_2O_5\ (g)\) is given as
\(N_2O_5(g) \rightarrow 2NO_2(g) + \frac{1}{2}O_2(g)\)
The above reaction is found to be of first order.
Select the correct statement for the half life of the given reaction

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.