At some instant, a radioactive sample $S_1$ having an activity $5\,\mu Ci$  has twice the number of nuclei as another sample $S_2$  which has an activity of  $10\,\mu Ci.$  The halflives of $S_1$  and  $S_2$ are

How long can an electric lamp of $100\; W$ be kept glowing by fusion of $2.0 \;kg$ of deuterium? Take the fusion reaction as

$_{1}^{2} H+_{1}^{2} H \rightarrow_{2}^{3} H e+n+3.27 \;M e V$

The half life of a radioactive substance is $5$ years. After $x$ years a given sample of the radioactive substance gest reduced to $6.25 \%$ of its initial value of $x$ is ...............

Radioactive material $'A'$ has decay constant $8 \lambda$ and material $'B'$ has decay constant $ ' \lambda '$. Initially they have same number of nuclei . After what time, the ratio of number of nuclei of material $'B'$ to that $'A'$ will be $\frac{1}{e}$ ?

For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\frac{d N}{d t}$ and $R=-\frac{d A}{d t}$, 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 number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an