Half-life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5 \, g$ of radium? (Atomic weight of radium $= 223$)

$A$ radioactive nuclide is produced at a constant rate of $n$ per second (e.g.,by bombarding a target with neutrons). If the number of nuclei at $t = 0$ is $N_0$,the number of nuclei $N$ at time $t$ is given by (where $\lambda$ is the decay constant):

Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay

$A$ radioactive nucleus $A$ with a half-life $T$ decays into a nucleus $B$. At $t = 0$,there is no nucleus $B$. At some time $t$,the ratio of the number of $B$ to that of $A$ is $0.3$. Then,$t$ is given by

The half-life of tritium is $ 12.5 $ years. What mass of tritium of initial mass $ 64 \ mg $ will remain undecayed after $ 50 $ years (in $mg$)?

The graph shows the $\log$ of activity $\log R$ of a radioactive material as a function of time $t$ in minutes. The half-life (in minutes) for the decay is closest to