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:

$A$ radioactive element will decay by $99\%$ between which of the following number of half-lives?

The activity of a radioactive material is $6.4 \times 10^{-4} \text{ curie}$. Its half-life is $5 \text{ days}$. The activity will become $5 \times 10^{-6} \text{ curie}$ after how many days?

Calculate the time (in $minutes$) interval between $33\%$ decay and $67\%$ decay if the half-life of a substance is $20\, minutes$.

Two radioactive isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.