The number of nuclei of a radioactive substance is $1000$ and $900$ at times $t = 0$ and $t = 2 \ s$,respectively. Then,the number of nuclei at time $t = 4 \ s$ will be:

The half-life of radium is $1600 \, \text{years}$. After how many years will $25 \, \text{g}$ of radium remain from $100 \, \text{g}$ of radium?

After five half-lives, the percentage of original radioactive atoms left is ...... $ \%$

The radiation emitted by a radioactive substance with a half-life of $30 \ min$ is measured by a Geiger-Muller counter. If the count rate drops to $5 \ \text{disintegrations/sec}$ in $2 \ \text{hours}$, find the initial disintegration rate.

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 ...... $\times 10^5$.

If one starts with $1 \, \text{curie}$ of a radioactive substance $(T_{1/2} = 12 \, \text{hrs})$, the activity left after a period of $1 \, \text{week}$ will be about: