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 $m_y$ ?

Unit of radioactivity is Rutherford. Its value is

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$

Mean life of a radioactive sample is $100$ seconds. Then its half life (in minutes) is

Carbon dating is best suited for determining the age of fossils if their age in years is of the order of