Number of nuclei of a radioactive substance at time $t = 0$ are $1000$ and $900$ at time $t = 2 \, s$. Then number of nuclei at time $t = 4 \, s$ will be

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

The ratio of the number of active nuclei of two different radioactive samples is $2:3$. Their half-lives are $1 \ h$ and $2 \ h$ respectively. The ratio of the number of active nuclei after $6 \ h$ will be:

Two radioactive elements $R$ and $S$ disintegrate as:
$R \rightarrow P + \alpha; \lambda_R = 4.5 \times 10^{-3} \, \text{years}^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 \times 10^{-3} \, \text{years}^{-1}$
Starting with the number of atoms of $R$ and $S$ in the ratio of $2:1$,what will be this ratio after the lapse of three half-lives of $R$?

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.

The activity of a radioactive material is $2.56 \times 10^{-3} \, Ci$. If the half-life of the material is $5 \, \text{days}$, after how many days will the activity become $2 \times 10^{-5} \, Ci$?