The half-life of a radioactive substance is $10 \, \text{minutes}$. If $n_1$ and $n_2$ are the number of atoms decayed in $20 \, \text{minutes}$ and $30 \, \text{minutes}$ respectively, then $n_1 : n_2 =$

If there is $0.1 \ mg$ of radioactive $Th^{234}$, how much of it will remain undecayed after $120 \ \text{days}$, given its half-life is $24 \ \text{days}$? (Answer in $\mu g$)

$A$ radioactive substance has a half-life of $3.8 \, days$. If the initial mass is $10.38 \, g$, how much mass (in grams) will remain after $19 \, days$?

$A$ 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 activity of a radioactive sample is $1.6 \, curie$ and its half-life is $2.5 \, days$. Its activity after $10 \, days$ will be .......... $curie$.

$A$ radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$,then the ratio $R/N$ varies with time as: