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

Draw a graph showing the variation of decay rate with number of active nuclei. 

The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 – t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is ……….$min$

A piece of wood from the ruins of an ancient building was found to have a $^{14}C$ activity of $12$ disintegrations per minute per gram of its carbon content. The $^{14}C$ activity of the living wood is $16$ disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of $^{14}C$ is $5760$ years.

The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30\, seconds$. Its half life is ………$seconds$