A certain radioactive nuclide of mass number $m_x$ disintegrates, with the emission of an electron and $\gamma$ radiation only, to give second nuclied of mass number $m_y.$ Which one of the following equation correctly relates $m_x$ and $m_y$ ?

The count rate of $10\,g$ of radioactive material was measured at different times and this has been shown in the figure. The half life of material and the total counts (approximately) in the first half life period, respectively are

Radioacitive nuclei $A$ and $B$ disintegrate into $C$ with half lives $T$ and $2T$. At $t = 0$, pumber of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when rate of disintegration of $A$ and $B$ are equal is

The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately ............ per minute

If half life of a radioactive element is $3\, hours$, after $9\, hours$ its activity becomes

State the relation between average life and decay constant.