JAMB Physics 2016 Paper

Concept:The half-life of a radioactive isotope is the time required for half of the sample to decay, calculated from its decay constant.Explanation:The half-life is given by the formula:$$t_{1/2} = \frac{\ln 2}{\lambda}$$where $\lambda$ is the decay constant. Since $\ln 2 \approx 0.693$, the formula becomes:$$t_{1/2} = \frac{0.693}{\lambda}$$Substitute the given decay constant $\lambda = 10^{-6}\ \text{s}^{-1}$:$$t_{1/2} = \frac{0.693}{10^{-6}}$$Dividing by $10^{-6}$ is the same as multiplying by $10^{6}$:$$t_{1/2} = 0.693 \times 10^{6}\ \text{s}$$$$t_{1/2} = 6.93 \times 10^{5}\ \text{s}$$This matches option B.Answer:$6.93 \times 10^{5}\ \text{s}$ (Option B).