$A$ 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

The half-life of radioactive $Po$ (Polonium) is $138.6 \, \text{days}$. For $1,000,000$ Polonium atoms, the number of disintegrations in $24 \, \text{hours}$ is:

Half-lives of two radioactive substances $A$ and $B$ are $20 \text{ minutes}$ and $40 \text{ minutes}$ respectively. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \text{ minutes}$,the ratio of the remaining number of $A$ and $B$ nuclei is:

For a radioactive material,its activity $A$ and rate of change of its activity $R$ are defined as $A = -\frac{dN}{dt}$ and $R = -\frac{dA}{dt}$,where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$) and $Q$ (mean life $2\tau$) have the same activity at $t = 0$. Their rates of change of activities at $t = 2\tau$ are $R_P$ and $R_Q$,respectively. If $\frac{R_P}{R_Q} = \frac{n}{e}$,then the value of $n$ is

The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text{th}}$ of its initial value in $30\, \text{years}$. The half-life of the radioactive element is $....\, \text{years}$.

At a certain moment,the amounts of two radioactive substances are in the ratio $2:1$. Their half-lives are $12 \text{ hours}$ and $16 \text{ hours}$ respectively. What will be the ratio of their remaining amounts after $2 \text{ days}$?