State the relation between average life and decay constant. 

$16\, gm$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hour$ and it was found that $1\, gm$ of the element remained (undisintegrated). Half life of the element is

A radioactive element ${ }_{92}^{242} X$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${ }_{ P }^{234} Y$. The value of $P$ is $………………$

The activity $R$ of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

$(i)$ Plot the graph of $R$ versus $t$ and calculate half-life from the graph.

$(ii)$ Plot the graph of $\ln \left( {\frac{R}{{{R_0}}}} \right) \to t$ versus $t$ and obtain the value of half-life from the graph.

$1\, Curie $ is equal to