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(C) The number of radioactive nuclei remaining after time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.Given that the mean life $	au = 1/\lambda$,the

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$10$

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(C) The number of radioactive nuclei remaining after time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.Given that the mean life $	au = 1/\lambda$,the time $t$ for two mean lives is $t = 2	au = 2/\lambda$.Substituting this into the decay equation: $N = N_0 e^{-\lambda(2/\lambda)} = N_0 e^{-2}$.Given $N_0 = 10 \, g$,the remaining mass is $N = 10 	imes e^{-2} \approx 10 	imes 0.135 = 1.35 \, g$.However,in a radioactive decay process,the daughter nuclei produced remain in the container unless they are gaseous or escape. Since the question asks for the total mass remaining in an open container,if the decay products are stable and solid,the total mass remains $10 \, g$ due to the conservation of mass.

$A$ radioactive substance of mass $10 \, g$ is kept in an open container. What is the approximate mass of the substance remaining in the container after two mean lives (in $, g$)?

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