$A$ radioactive element has a half-life of $1 \text{ day}$. After $3 \text{ days}$,the amount of the element left will be:

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

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 .......... $days$.

The half-life period of radioactive decay of ${}^{14}C$ is $5730 \ years$. An archaeological artifact contains $80\%$ of ${}^{14}C$ as compared to a living tree. Calculate the age of the sample in $years$.

Radium has an atomic weight of $226$ and a half-life of $1600$ years. The number of disintegrations produced per second from $1 \ g$ of radium is:

Half-life is the time in which $50\%$ of a radioactive element disintegrates. Carbon-$14$ disintegrates $50\%$ in $5770$ years. Find the half-life of carbon-$14$ in years.