Which sample contains greater number of nuclei?

a 5.00- $\mathrm{\mu }$Ci sample of ${}^{240}\mathrm{Pu}$  (half-life 6560y)

or a 4.45- $\mathrm{\mu }$Ci sample of ${}^{243}\mathrm{Am}$  (half-life 7370y)

The activity $\left(-\frac{\mathrm{dN}}{\mathrm{dt}}\right)=\mathrm{\lambda N}\Rightarrow \mathrm{N}=\left(-\frac{\mathrm{dN}}{\mathrm{dt}}\right)\left(\frac{{\mathrm{T}}_{1/2}}{{\log }_{\mathrm{e}}2}\right)$

Taking the ratio of this expression for ${}^{240}\mathrm{Pu}$ to this same expression for ${}^{243}\mathrm{Am}$.

$\frac{{\mathrm{N}}_{\mathrm{Pu}}}{{\mathrm{N}}_{\mathrm{Am}}}=\frac{\left(-{\displaystyle \frac{{\mathrm{dN}}_{\mathrm{Pu}}}{\mathrm{dt}}}\right){\left({\mathrm{T}}_{1/2}\right)}_{\mathrm{Pu}}}{\left(-{\displaystyle \frac{{\mathrm{dN}}_{\mathrm{Am}}}{\mathrm{dt}}}\right){\left({\mathrm{T}}_{1/2}\right)}_{\mathrm{Am}}}$

$=\frac{\left(5\mathrm{\mu Ci}\right) \mathrm{x} \left(6560\mathrm{y}\right)}{\left(4.45\mathrm{\mu Ci}\right) \mathrm{x} \left(7370\mathrm{y}\right)}=1$

i.e., the two samples contains equal number of nuclei.