At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$?

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9$ years. Find the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9$ years (given $2^{1/3} = 1.26$).

The $S.I.$ unit of radioactivity is

The ratio of the number of active nuclei in two different samples is $2:3$. Their half-lives are $2 \ hours$ and $3 \ hours$ respectively. After $12 \ hours$,the ratio of their activities will be:

Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$,respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

The decay constant of a radioisotope is $\lambda$. If $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$ respectively,what is the number of nuclei that have decayed during the time interval $(t_1 - t_2)$?