(half-life = 12.8 h) decays by emission (32%), emission (19%) and electron capture (49%). The partia — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

The overall decay constant is $\lambda_{total} = \lambda_{\beta^-} + \lambda_{\beta^+} + \lambda_{EC}$. We know $\lambda_{\beta^-} = 0.32 \lambda_{total}$. The partial half-life relates to the partial decay constant via $t_{1/2,\beta^-} = \frac{\ln 2}{\lambda_{\beta^-}} = \frac{\ln 2}{0.32 \lambda_{total}} = \frac{t_{1/2, total}}{0.32} = \frac{12.8}{0.32} = 40 \text{ h}$. Therefore, correct answer is 0040.