A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is

If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is

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

Half-life of a radioactive substance is $20\,minute$ . The time between $20\%$ and $80\%$ decay will be ……… $min$

The '$rad$' is the correct unit used to report the measurement of