The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30 \, s$. Its half-life is ......... $s$.

An alloy is composed of two radioactive materials $A$ and $B$ having equal weight. The half-lives of $A$ and $B$ are $10 \ yrs$ and $20 \ yrs$ respectively. After time $t$, the alloy was found to consist of $(1/e) \ kg$ of $A$ and $1 \ kg$ of $B$. If the atomic weights of $A$ and $B$ are the same, then the value of $t$ is (Assume $\ln 2 = 0.7$):

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

If the half-life of a radioactive atom is $2.3 \, days$,then its decay constant would be

The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

The activity of a radioactive material is $2.56 \times 10^{-3} \, Ci$. If the half-life of the material is $5 \, \text{days}$, after how many days will the activity become $2 \times 10^{-5} \, Ci$?