The half-life period of a radioactive element is $10$ days. How long does it take for $90\%$ of a given mass of this element to disintegrate?

If the decay or disintegration constant of a radioactive substance is $\lambda$,then its half-life and mean life are respectively $(log_e 2 = \ln 2)$.

If the half-life of a radioactive element is $12.5 \ h$,then the time taken to disintegrate $256 \ g$ of the substance into $1 \ g$ is (in hours)

$99\%$ of the nuclei of a radioactive element decay between which of the following times?

The activity $R$ of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

$t (h)$	$0$	$1$	$2$	$3$	$4$
$R (MBq)$	$100$	$35.36$	$12.51$	$4.42$	$1.56$

$(i)$ Plot the graph of $R$ versus $t$ and calculate the half-life from the graph.
$(ii)$ Plot the graph of $\ln \left( \frac{R}{R_0} \right)$ versus $t$ and obtain the value of the half-life from the graph.

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.