The half-life of $^{238} _{92} U$ undergoing $\alpha$ -decay is $4.5 \times 10^{9}$ $years$. What is the activity of $1\; g$ sample of $^{238} _{92} U$?

A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 × 10^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 ×10^9$ years (given $2^{1/3} = 1.26$)

The fossil bone has a ${}^{14}C:{}^{12}C$ ratio, which is $\left[ {\frac{1}{{16}}} \right]$ of that in a living animal bone. If the halflife of ${}^{14}C$ is $5730\, years$, then the age of the fossil bone is ……….$years$

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?

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

A radioactive material has a half-life of $8$ years. The activity of the material will decrease to about $1/8$ of its original value in ………. $years$