After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half-lives $1$ month and $2$ months respectively. At time $t=0$,the number of nuclei of each $P$ and $Q$ is $x$. At the time when the rates of disintegration of $P$ and $Q$ are equal,the number of nuclei of $R$ is ........ $x$.

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

At some instant,a radioactive sample $S_1$ having an activity $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ are:

Two radioactive substances $X$ and $Y$ initially contain equal number of nuclei. $X$ has a half-life of $1\, hour$ and $Y$ has a half-life of $2\, hours$. After $2\, hours$,the ratio of the activity of $X$ to the activity of $Y$ is

The half-life period of a radioactive substance is $60 \ days$. The time taken for $\frac{7}{8}$ of its original mass to disintegrate will be $...... \ days$.