$A$ radioactive element with half-life $6.5 \ hr$ has $48 \times 10^{19}$ atoms. Number of atoms left after $26 \ hr$ is:

The half-life of $_6C^{14}$,if its decay constant is $6.31 \times 10^{-4} \ yr^{-1}$,is ....... $yrs$.

The Carbon-$14$ dating method is based on the fact that:

$A$ radioactive element decays at such a rate that after $15 \ min$ only $1/10$ of the original amount is left. How many more minutes will be needed when only $1/100$ of the original amount will be left? .......... $\min$

$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

What is the value of the decay constant of a compound having a half-life time $T_{1/2} = 2.95 \text{ days}$?