The activity of a radioactive sample falls from $700 \; s^{-1}$ to $500 \; s^{-1}$ in $30 \; min$. Its half-life is close to ......... $min$.

$A$ radioactive element emits $200$ particles per second. After $3$ hours,$25$ particles per second are emitted. The half-life period of the element will be .......... $minutes$.

The graph shows $\ln \left| \frac{dN(t)}{dt} \right|$ versus $t$ for a radioactive sample. If the number of radioactive nuclei decreases by a factor of $p$ after $4.16$ years,then $p = $.....

Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

Give the different units of radioactivity and define them.

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.