A sample of a radioactive nucleus $A$ disintegrates to another radioactive nucleus $B$, which in turn disintegrates to some other stable nucleus $C.$ Plot of a graph showing the variation of number of atoms of nucleus $B$ vesus time is :

(Assume that at ${t}=0$, there are no ${B}$ atoms in the sample)

In a radioactive material, fraction of active material remaining after time $t$ is $\frac{9}{16}$ The fraction that was remaining after $\frac{t}{2}$ is 

A radioactive material has an initial amount $16\, gm$. After $120$ days it reduces to $1 \,gm$, then the half-life of radioactive material is ..........$days$

The half life of radioactive Radon is $3.8\, days$. The time at the end of which $1/20^{th}$ of the Radon sample will remain undecayed is  ............ $days$ (Given $log_{10}e = 0.4343$ )

In a radioactive decay chain, ${ }_{90}^{232} Th$ nucleus decays to ${ }_{82}^{212} Pb$ nucleus. Let $N _\alpha$ and $N _\beta$ be the number of $\alpha$ and $\beta^{-}$particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

$(A)$ $N _\alpha=5$  $(B)$ $N _\alpha=6$  $(C)$ $N _\beta=2$  $(D)$ $N _\beta=4$

The half-life of radium is about $1600$ years. Of $100\, g$ of radium existing now, $25\, g$ will remain unchanged after .......... $years$