The expression \( t_{1/2}=\frac{0.693}{k} \) is valid for........order reaction.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → first
The half-life, t1/2, is the time in which the concentration of a reactant falls to half its initial value. Putting [R] = [R]0/2 into the integrated rate equation of a first order reaction gives t1/2 = 0.693/k.
This half-life does not contain [R]0: it is independent of the initial concentration. So the expression is valid for a first order reaction.
Why the other options are incorrect
Option (1) zero — Incorrect. For a zero order reaction, t1/2 = [R]0/2k, which is proportional to the initial concentration.
Option (3) half — Incorrect. For any order other than first, t1/2 depends on the initial concentration, so it cannot be 0.693/k.
Option (4) second — Incorrect. For a second order reaction, t1/2 = 1/(k[R]0), which is inversely proportional to the initial concentration.
NCERT (2026-27 edition):
Half-Life of a Reaction – …
