$A$ radioactive element has a half-life period of $800$ years. After $6400$ years,what fraction of the initial amount will remain?

The half-life of a radioactive isotope $X$ is $1.37 \times 10^9 \, y$. It decays to a stable isotope $Y$. In a rock sample from the moon,the ratio of $X$ to $Y$ is $1:7$. The age of the rock is:

The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be:

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5\, \text{minutes}$. The time (in minutes) at which the activity reduces to half of its initial value is

If $10\%$ of a radioactive material decays in $5\, days$,then the amount of the original material left after $20\, days$ is approximately .......... $\%$

Radon $({Rn})$ decays into Polonium $({Po})$ by emitting an $\alpha$-particle with a half-life of $4\, days$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12\, days$,the number of atoms of $Rn$ left in the sample will be: