The decay constant of a radioactive element is $0.01$ per second. Its half life period is …….$sec$

Half life of $B{i^{210}}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left over after $10$ days is

Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time

At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively 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 ${ }^{131} \mathrm{I}$ is injected into the blood of a person. The activity of the amount of ${ }^{131} \mathrm{I}$ injected was $2.4 \times 10^5$ Becquerel $(\mathrm{Bq})$. 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, $2.5 \mathrm{ml}$ of blood is drawn from the person's body, and gives an activity of $115 \mathrm{~Bq}$. The total volume of blood in the person's body, in liters is approximately (you may use $\mathrm{e}^{\mathrm{x}} \approx 1+\mathrm{x}$ for $|\mathrm{x}| \ll 1$ and $\ln 2 \approx 0.7$ ).