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(C) 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 un

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$\frac{N_1 T_2}{N_2 T_1}$

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(C) 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 $\lambda = \frac{\ln 2}{T}$.For the two radioactive elements,the activities are:$A_1 = \lambda_1 N_1 = \frac{\ln 2}{T_1} N_1$$A_2 = \lambda_2 N_2 = \frac{\ln 2}{T_2} N_2$The ratio of their activities is:$\frac{A_1}{A_2} = \frac{(\frac{\ln 2}{T_1}) N_1}{(\frac{\ln 2}{T_2}) N_2}$Simplifying the expression:$\frac{A_1}{A_2} = \frac{N_1}{T_1} 	imes \frac{T_2}{N_2} = \frac{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 that instant is

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