$A$ piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of $^{14}C$ is $t_{1/2} = 5760$ years)

If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .

If a radioactive substance decays $10 \%$ in every $16 \text{ hours}$,then the percentage of the radioactive substance that remains after $2 \text{ days}$ is

In a radioactive decay process,the activity is defined as $A = -\frac{dN}{dt}$,where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources,$S_1$ and $S_2$,have the same activity at time $t = 0$. At a later time,the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$,respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd}}$ and $7^{\text{th}}$ half-lives,respectively,the ratio $A_1/A_2$ is:

Find the time in years required for $10\%$ of a radioactive sample to decay,given that its half-life is $22 \text{ years}$.

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For $10^6$ Polonium atoms,the number of disintegrations in $24$ hours is: