After $1$ hour,$1/16$ of the radioactive substance remains. Its half-life is ....... minutes.

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:

The half-life of a radioactive element is $10 \ h$. The fraction of initial radioactivity of the element that will remain after $40 \ h$ is

At a certain moment,the amounts of two radioactive substances are in the ratio $2:1$. Their half-lives are $12 \text{ hours}$ and $16 \text{ hours}$ respectively. What will be the ratio of their remaining amounts after $2 \text{ days}$?

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:

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where $\lambda$ is the decay constant)