Calculate the half-life of a first order reaction from the rate constants given below:
$(i) \ 200 \ s^{-1}$
$(ii) \ 2 \ min^{-1}$
$(iii) \ 4 \ years^{-1}$

$(i) \ \text{Half-life}, t_{1/2} = \frac{0.693}{k} = \frac{0.693}{200 \ s^{-1}} = 3.465 \times 10^{-3} \ s \approx 3.47 \times 10^{-3} \ s$
$(ii) \ \text{Half-life}, t_{1/2} = \frac{0.693}{k} = \frac{0.693}{2 \ min^{-1}} = 0.3465 \ min \approx 0.35 \ min$
$(iii) \ \text{Half-life}, t_{1/2} = \frac{0.693}{k} = \frac{0.693}{4 \ years^{-1}} = 0.17325 \ years \approx 0.173 \ years$