If one starts with $1 \, \text{curie}$ of a radioactive substance $(T_{1/2} = 12 \, \text{hrs})$, the activity left after a period of $1 \, \text{week}$ will be about:

Half-lives of two radioactive elements $A$ and $B$ are $20 \ min$ and $40 \ min$,respectively. Initially,the samples have equal number of nuclei. After $80 \ min$,the ratio of decayed number of $A$ and $B$ nuclei will be

The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5\, minutes$,the rate becomes $1250$ disintegrations per minute. Then,its decay constant (per minute) is

$A$ radioactive element has a rate of disintegration of $8000$ disintegrations per minute at a particular instant. After $4$ minutes,it becomes $2000$ disintegrations per minute. The decay constant per minute is: (in $log _e 2$)

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: