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(D) The activity $R$ of a radioactive sample is defined as the rate of decay,given by $R = \lambda N$,where $\lambda$ is the decay constant and $N$ is

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$\frac{N_{1} T_{2}}{N_{2} T_{1}}$

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(D) The activity $R$ of a radioactive sample is defined as the rate of decay,given by $R = \lambda N$,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 formula $\lambda = \frac{\ln 2}{T}$.Substituting this into the activity formula,we get $R = \frac{(\ln 2) N}{T}$.For the two elements,the activities are:$R_{1} = \frac{(\ln 2) N_{1}}{T_{1}}$$R_{2} = \frac{(\ln 2) N_{2}}{T_{2}}$The ratio of their activities is:$\frac{R_{1}}{R_{2}} = \frac{(\ln 2) N_{1} / T_{1}}{(\ln 2) N_{2} / T_{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 this instant is

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