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

If the mass of a radioactive sample is doubled, the activity of the sample and the disintegration constant of the sample are respectively

Certain radio-active substance reduces to $25\%$ of its value in $16$ days. Its half-life is ........ $days$ 

At time $t=0$, a material is composed of two radioactive atoms ${A}$ and ${B}$, where ${N}_{{A}}(0)=2 {N}_{{B}}(0)$ The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to ${B}$ and ${B}$ disintegrates to ${C}$. Which of the following figures represents the evolution of ${N}_{{B}}({t}) / {N}_{{B}}(0)$ with respect to time $t$ ?

${N}_{{A}}(0)={No} . \text { of } {A} \text { atoms at } {t}=0$

${N}_{{B}}(0)={No} . \text { of } {B} \text { atoms at } {t}=0$

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half its value is 

Give a brief explanation about radioactivity.