The nuclide $^{131}I$ is radioactive, with a half-life of $8.04$ days. At noon on January $1$, the activity of a certain sample is $60089$. The activity at noon on January $24$ will be

Two radioactive substances $X$ and $Y$ originally have $N _{1}$ and $N _{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{ N _{1}}{ N _{2}}$ will be equal to

A radioactive material has an initial amount $16\, gm$. After $120$ days it reduces to $1 \,gm$, then the half-life of radioactive material is ……….$days$

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : …………..$\%$

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.