If the half-life of radium is $77$ days,its decay constant in $day^{-1}$ will be:

The half-life of a substance is $20 \ min$. The time taken between $33\%$ decay and $67\%$ decay will be ....... $min$.

The half-life period of a radioactive sample is $T$. If a fraction $x$ disintegrates in time $t$,what fraction will decay in time $\frac{t}{2}$?

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:

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 $\ln 2 = 0.7$):

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.