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 $7370 \ y$)?

$A$ radioactive element has a half-life period of $800$ years. After $6400$ years,what fraction of the initial amount will remain?

$A$ fraction $f_1$ of a radioactive sample decays in one mean life,and a fraction $f_2$ decays in one half-life.

Two radioactive materials $A$ and $B$ having decay constants $7 \lambda$ and $\lambda$ respectively,initially have the same number of nuclei. The time taken for the ratio of the number of nuclei of material $B$ to that of $A$ to be $e$ is:

For a radioactive material,its activity $A$ and rate of change of its activity $R$ are defined as $A = -\frac{dN}{dt}$ and $R = -\frac{dA}{dt}$,where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$) and $Q$ (mean life $2\tau$) have the same activity at $t = 0$. Their rates of change of activities at $t = 2\tau$ are $R_P$ and $R_Q$,respectively. If $\frac{R_P}{R_Q} = \frac{n}{e}$,then the value of $n$ is

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of: