Which sample contains a greater number of nuclei: a $5.00 \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \ y$) or a $4.45 \mu Ci$ sample of $^{243}Am$ (half-life $7370 \ y$)?

The half-life of a radioactive substance is $5$ years. After $x$ years,a given sample of the radioactive substance gets reduced to $6.25 \%$ of its initial value. The value of $x$ is ...............

The activity of a radioactive sample is $1.6 \, curie$ and its half-life is $2.5 \, days$. Its activity after $10 \, days$ will be .......... $curie$.

${ }^{131} I$ is an isotope of Iodine that $\beta$ decays to an isotope of Xenon with a half-life of $8$ days. $A$ small amount of a serum labelled with ${ }^{131} I$ is injected into the blood of a person. The activity of the amount of ${ }^{131} I$ injected was $2.4 \times 10^5 \text{ Bq}$. It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After $11.5$ hours,$2.5 \text{ ml}$ of blood is drawn from the person's body,and gives an activity of $115 \text{ Bq}$. The total volume of blood in the person's body,in liters,is approximately (you may use $e^{x} \approx 1+x$ for $|x| \ll 1$ and $\ln 2 \approx 0.7$):

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?