A zero order reaction (rate constant $k_{0}$ ) and a first order reaction (rate constant $k_{1}$ ) have the same initial concentration $[A]_{0}$ and the same initial rate. The ratio $t_{1/2} (zero order) / t_{1/2} (first order)$ is (use $ln 2 = 0.693$ )

Answer: C

Equal initial rates give

k_{0} = k_{1} [A]_{0}

. Then

t_{1/2} (0) = [A]_{0} /2 k_{0} = 1/ (2 k_{1})

and

t_{1/2} (1) = 0.693/ k_{1}

. The ratio is

0.5/0.693 = 0.7215 \approx 0.72