$A$ certain nuclide has a half-life of $25 \ min$. If one starts with $100 \ g$ of it,how much of it will remain at the end of $100 \ min$?

$A$ certain nuclide has a half-life period of $30 \ minutes$. If a sample containing $600$ atoms is allowed to decay for $90 \ minutes$,how many atoms will remain?

The ratio of the amount of two elements $X$ and $Y$ at radioactive equilibrium is $1 : 2 \times 10^{-6}$. If the half-life period of element $Y$ is $4.9 \times 10^{-4} \ days$,then the half-life period of element $X$ will be .......... $days$.

If $2.0 \ g$ of a radioactive isotope has a half-life of $20 \ hr$,the half-life of $0.5 \ g$ of the same substance is ........ $hr$.

The decay of $_{92}U^{235}$ is a reaction of .......... order.

$A$ wood piece is $11460$ years old. What is the fraction of $^{14}C$ activity left in the piece? (Half-life period of $^{14}C$ is $5730$ years)