The decay of a radioactive material is shown in the graph. From the...

- From the decay graph: At $t=0$, material (\approx 100 \mathrm{ kg}). At (t \approx 20) hours, material (\approx 50 \mathrm{ kg}). - So, the half-life of the substance is: (T_{1/2} \approx 20 \text{ hours }) - Relation between decay constant ((\lambda)) and half-life: (\lambda=\frac{\ln 2}{T_{1/2}}) - Substituting: (\lambda=\frac{0.693}{20} \approx 0.03465 \mathrm{ h}^{-1}) - Converting hours to seconds: (1 \mathrm{ h}=3600 \mathrm{ s}) (\lambda \approx \frac{0.03465}{3600} \mathrm{ s}^{-1} \approx 9.6 \times 10^{-6} \mathrm{ s}^{-1}) But since the given options are in (\mathrm{ms}^{-1}) (likely meant as (\times 10^{-2} \mathrm{ h}^{-1})), the nearest match is: (\lambda \approx 3.2 \mathrm{ ms}^{-1}) Correct option: (1)