The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

The average life $T$ and the decay constant $\lambda$ of a radioactive nucleus are related as

In a radioactive material,the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$,it is $R_{2}$. If the decay constant of the material is $\lambda$,then:

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

The activity of a radioactive sample decreases to $\left(\frac{1}{3}\right)$ of its original value in $3 \ days$. Then,in $9 \ days$,its activity reduces to:

Two samples $A$ and $B$ contain equal amount of radioactive substances. If $(1/8)^{th}$ of sample $A$ and $(1/128)^{th}$ of sample $B$ remain after $9 \text{ hours}$, then the ratio of half-life period of $B$ to that of $A$ is