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(B) The decay constant $\lambda$ for a process is given by $\lambda = \frac{\ln 2}{T_{1/2}}$.For two parallel decay processes, the effective decay con

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$18$

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(B) The decay constant $\lambda$ for a process is given by $\lambda = \frac{\ln 2}{T_{1/2}}$.For two parallel decay processes, the effective decay constant is $\lambda_{	ext{eff}} = \lambda_1 + \lambda_2$.Given $T_1 = 0.7 \ hr$ and $T_2 = 0.3 \ hr$, and $\ln 2 = 0.7$.Then $\lambda_1 = \frac{0.7}{0.7} = 1 \ hr^{-1}$ and $\lambda_2 = \frac{0.7}{0.3} = \frac{7}{3} \ hr^{-1}$.Effective decay constant $\lambda_{	ext{eff}} = 1 + \frac{7}{3} = \frac{10}{3} \ hr^{-1}$.The effective average life $	au_{	ext{eff}}$ is the reciprocal of the effective decay constant:$	au_{	ext{eff}} = \frac{1}{\lambda_{	ext{eff}}} = \frac{1}{10/3} = 0.3 \ hr$.Converting to minutes: $	au_{	ext{eff}} = 0.3 	imes 60 \ min = 18 \ min$.

$A$ radioactive nucleus can decay in two different processes with half-lives of $0.7 \ hr$ and $0.3 \ hr$. The effective average life of the nucleus in minutes is approximately (value of $\ln 2 = 0.7$):

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