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

Two radioactive elements $A$ and $B$ initially have the same number of atoms. The half-life of $A$ is equal to the mean life of $B$. If $\lambda_A$ and $\lambda_B$ are the decay constants of $A$ and $B$ respectively,then choose the correct relation from the given options.

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 unit of radioactivity is Rutherford. Its value is:

The half-life of a radioactive substance is $20 \ min$. The approximate time interval $(t_{2}-t_{1})$ between the time $t_{2}$,when $2/3$ of it has decayed,and time $t_{1}$,when $1/3$ of it has decayed,is (in $min$):

The half-life of a sample of a radioactive substance is $1 \text{ hour}$. If $8 \times 10^{10}$ atoms are present at $t = 0$,then the number of atoms decayed in the duration $t = 2 \text{ hours}$ to $t = 4 \text{ hours}$ will be