The decay constant of a radioactive element is $1.5 \times {10^{ – 9}}$ per second. Its mean life in seconds will be

The initial activity of a certain radioactive isotope was measured as $16000\ counts\  min^{-1}$. Given that the only activity measured was due to this isotope and that its activity after $12\, h$ was $2000\ counts\ min^{-1}$, its half-life, in hours, is nearest to

A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life time of one species is $\tau$ and that of the other is $5 \tau$. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot

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.

Radon $({R_n})$ decays into Polonium (${P_0}$) by emitting an $\alpha – $ particle with half-life of $4\, days$. A sample contains $6.4 \times {10^{10}}$ atoms of $R_n$. After $12\, days$, the number of atoms of ${R_n}$ left in the sample will be