The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$ . The half-life of $X$ is $\tau $ . The growth curve for $Y$ intersects the decay curve for $X$ after time $T$ . What is the time $T$ ?
$\frac {\tau }{2}$
$In\left( {\frac{\tau }{2}} \right)$
$\tau $
$2\tau $
The radioactive sources $A$ and $B$ have half lives of $2\ hr$ and $4\ hr$ espectively, initially contain the same number of radioactive atoms. At the end of $2\ hours$, their rates of distintegration are in the ratio
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 $..................$
$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$
The half-life of a radioactive substance is $30$ minutes. The times (in minutes ) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is
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 $m_y$ ?