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(A) The activity $R$ of a radioactive substance at any time $t$ is given by the law of radioactive decay: $R(t) = R_0 e^{-\lambda t}$.At time $t_1$, t

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$e^{-\lambda(t_2 - t_1)}$

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(A) The activity $R$ of a radioactive substance at any time $t$ is given by the law of radioactive decay: $R(t) = R_0 e^{-\lambda t}$.At time $t_1$, the activity is $R_1 = R_0 e^{-\lambda t_1}$.At time $t_2$, the activity is $R_2 = R_0 e^{-\lambda t_2}$.To find the ratio $\frac{R_2}{R_1}$, we divide the two expressions:$\frac{R_2}{R_1} = \frac{R_0 e^{-\lambda t_2}}{R_0 e^{-\lambda t_1}}$$\frac{R_2}{R_1} = e^{-\lambda t_2} \cdot e^{\lambda t_1}$$\frac{R_2}{R_1} = e^{-\lambda(t_2 - t_1)}$.

Activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$ $(t_2 > t_1)$. Then the ratio $\frac{R_2}{R_1}$ is:

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