Which sample contains a greater number of nuc | vedclass

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(C) The activity $R$ is given by $R = \lambda N$,where $\lambda = \frac{\ln 2}{T_{1/2}}$.Thus,the number of nuclei $N$ is given by $N = \frac{R}{\lamb

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Equal in both

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(C) The activity $R$ is given by $R = \lambda N$,where $\lambda = \frac{\ln 2}{T_{1/2}}$.Thus,the number of nuclei $N$ is given by $N = \frac{R}{\lambda} = R 	imes \frac{T_{1/2}}{\ln 2}$.For $^{240}Pu$: $N_{Pu} = R_{Pu} 	imes \frac{(T_{1/2})_{Pu}}{\ln 2} = 5.00 \mu Ci 	imes \frac{6560 \ y}{\ln 2}$.For $^{243}Am$: $N_{Am} = R_{Am} 	imes \frac{(T_{1/2})_{Am}}{\ln 2} = 4.45 \mu Ci 	imes \frac{7370 \ y}{\ln 2}$.Calculating the ratio: $\frac{N_{Pu}}{N_{Am}} = \frac{5.00 	imes 6560}{4.45 	imes 7370} = \frac{32800}{32796.5} \approx 1$.Since the ratio is approximately $1$,both samples contain an equal number of nuclei.

Which sample contains a greater number of nuclei: a $5.00 \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \ y$) or a $4.45 \mu Ci$ sample of $^{243}Am$ (half-life $7370 \ y$)?

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