If the half life of a radioactive sample is $10\, hours$, its mean life is ..........$hours$

The decay constant of a radio isotope is $\lambda$. If  $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$  respectively, the number of nuclei which have decayed during the time $(t_1 - t_2)$ 

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

Define the average life of a radioactive substance. 

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

The half-life of a radioactive substance is $40$ years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant