A radioactive sample with a half life of $1$ month has the label : “Activity$=2\, micro\,\,curies$ on $1-8-1991$.'' What will be its activity two months earlier ............ $micro\,\, curies$.

A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is  ........ $\times 10^{16}$ 

The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially both of them have the same number of atoms. Then

The half life of radium is $1620$ years and its atomic weight is $226\, k\,gm$ per kilomol. The number of atoms that will decay from its $1\, gm$ sample per second will be

(Avogadro's number $N = 6.02 \times {10^{26}}$atom/kilomol)

In a radioactive decay process, the activity is defined as $A=-\frac{\mathrm{d} N}{\mathrm{~d} t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have 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. . . . . . .

The half-life of a particle of mass $1.6 \times 10^{-26} \,kg$ is $6.9 \,s$ and a stream of such particles is travelling with the kinetic energy of a particle being $0.05 \,eV$. The fraction of particles which will decay, when they travel a distance of $1 \,m$ is