The curve between the activity $A$ of a radioactive sample and the number of active atoms $N$ is

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$. If $\lambda$ is the decay constant,then which of the following is correct?

$A$ radioactive sample has a half-life of $5 \text{ years}$. The percentage of the fraction decayed in $10 \text{ years}$ will be: (in $\%$)

The decay constant of radium is $\lambda$. By a suitable process,its compound radium bromide is obtained. The decay constant of radium bromide will be:

${ }^{131} I$ 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 $\ln 2 \approx 0.7$):

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is