A radioactive material decays by simultaneous emissions of two particles with half lives of $1400\, years$ and $700\, years$ respectively. What will be the time after which one third of the material remains? (Take In $3=1.1$ ) (In $years$)

The half life of a radioactive sample undergoing $\alpha$ - decay is $1.4 \times 10^{17}$ s. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly

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.

Write and derive the law of radioactivity decay. 

What is radioactivity ?

A radioactive sample disintegrates via two independent decay processes having half lives $T _{1 / 2}^{(1)}$ and $T _{1 / 2}^{(2)}$ respectively. The effective half- life $T _{1 / 2}$ of the nuclei is