$A$ radioactive element $X$ converts into another stable element $Y$. The half-life of $X$ is $2 \text{ hours}$. Initially,only $X$ is present. After a time $t$,if the ratio of atoms of $X$ to $Y$ is $1:4$,then the value of $t$ is

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their disintegration constants are in the ratio of $1 : 2.$ What should be the ratio of the number of atoms of the two at time $t = 0$ so that the probabilities of getting $\alpha$ and $\beta$ particles are the same at time $t = 0$?

If the decay or disintegration constant of a radioactive substance is $\lambda$,then its half-life and mean life are respectively:

The activity of a radioactive sample is $1.6 \, curie$ and its half-life is $2.5 \, days$. Its activity after $10 \, days$ will be .......... $curie$.

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:

State the law of radioactive decay.