The decay constant for the nuclide $^{64}Cu$ is $1.6 \times 10^{-5} \, s^{-1}$. Find the activity of a $1 \, mg$ sample of $^{64}Cu$ in $Ci$. (Given: Atomic mass of Copper = $64 \, g/mol$,$1 \, Ci = 3.7 \times 10^{10} \, Bq$)

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

$A$ radioactive substance contains $10000$ nuclei and its half-life period is $20$ days. The number of nuclei present at the end of $10$ days is

The half-life of radium is $1600$ years. Its mean life will be ....... years.

The specific activity of $Ra^{226}$ is $1 \, Ci/g$. The activity of $1 \, \mu g$ of $Ra^{226}$ will be:

In a radioactive decay process,the activity is defined as $A = -\frac{dN}{dt}$,where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources,$S_1$ and $S_2$,have the same activity at time $t = 0$. At a later time,the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$,respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd}}$ and $7^{\text{th}}$ half-lives,respectively,the ratio $A_1/A_2$ is: