In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. The activity of the sample varies with time according to which curve?

After five half-lives,what will be the fraction of the initial substance remaining?

Two radioactive materials $X_1$ and $X_2$ 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 $X_1$ to that of $X_2$ will be $1 / e$ after a time:

Two radioactive substances $A$ 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:

$A$ piece of wood from the ruins of an ancient building was found to have a $^{14}C$ activity of $12$ disintegrations per minute per gram of its carbon content. The $^{14}C$ activity of the living wood is $16$ disintegrations per minute per gram. How long ago did the tree,from which the wooden sample came,die? Given half-life of $^{14}C$ is $5760$ years.

The half-life of the isotope $_{11}Na^{24}$ is $15 \, hrs$. How much time does it take for $\frac{7}{8}$ of a sample of this isotope to decay?