The relation between half-life $(T)$ and decay constant $(\lambda)$ is

The half-life of a radioactive substance is $100 \ s$. How many grams of the radioactive substance will remain after $5 \ min$ if the initial amount is $8 \ g$ (in $g$)?

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.

Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is ................ $minutes$.

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be:

The half-life of $Bi^{210}$ is $5$ days. If we start with $50,000$ atoms of this isotope,the number of atoms left over after $10$ days is: