If the radioactive decay constant of radium is $1.07 \times 10^{-4}$ per year,then its half-life period is approximately equal to ......... $years$.

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

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion $5$ billion years ago. The other was created in a nuclear reactor $5$ minutes ago. The probability of decay during the next time interval is

At some instant,a radioactive sample $S_1$ having an activity $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ are:

The half-life of a radioactive substance is $20 \text{ minutes}$. In $........ \text{ minutes}$ time,the activity of the substance drops to $\left(\frac{1}{16}\right)^{th}$ of its initial value.

Given below are two statements:
Statement $I$: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is directly proportional to the total number of nuclei in the sample.
Statement $II$: The half-life of a radionuclide is the time required for the number of radioactive nuclei to reduce to half of its initial value at time $t = 0$.
In the light of the above statements, choose the most appropriate answer from the options given below: