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(B) The activity $A$ of a radioactive sample is given by the formula $A = \lambda N$, where $\lambda$ is the decay constant and $N$ is the number of u

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$N_1T_2/N_2T_1$

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(B) The activity $A$ of a radioactive sample is given by the formula $A = \lambda N$, where $\lambda$ is the decay constant and $N$ is the number of undecayed atoms.The decay constant $\lambda$ is related to the half-life $T$ by the relation $\lambda = \ln(2) / T$.Therefore, the activity $A$ can be expressed as $A = (\ln(2) / T) 	imes N$.For the two elements, the activities are $A_1 = (\ln(2) / T_1) 	imes N_1$ and $A_2 = (\ln(2) / T_2) 	imes N_2$.The ratio of their activities is $A_1 / A_2 = [(\ln(2) / T_1) 	imes N_1] / [(\ln(2) / T_2) 	imes N_2]$.Simplifying this, we get $A_1 / A_2 = (N_1 / T_1) 	imes (T_2 / N_2) = (N_1 T_2) / (N_2 T_1)$.

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively, present at a given instant. The ratio of their activities at this instant is

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