The half-life of $^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{{1}}{{16}} \,th$ of its initial value is .........$\mu s$

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

At time $t = 0, N_1$ nuclei of decay constant $\lambda _1 \,\& \,N_2$ nuclei of decay constant $\lambda _2$ are mixed . The decay rate of the mixture is :

Write down the definition and formula of half life of radioactive substance.

Radioactivity was discovered by

Define the average life of a radioactive sample and obtain its relation to decay constant and half life.