The graph in figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t.$ The relationship between $A$ and $t$ is : $($ Assume $ln\,\, 12 = 2.6)$
$A = 2.6 \,e^{-10t}$
$A = 12 \,e^{-10t}$
$A = 2.6 \,e^{-0.1t}$
$A = 1.2 \,e^{-0.1t}$
The activity of a sample of a radioactive material is ${A_1}$ at time ${t_1}$ and ${A_2}$ at time ${t_2}$ $({t_2} > {t_1}).$ If its mean life $T$, then
At time $t=0$, a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition, $c$ numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$ ?
In Fig. $X$ represents time and $Y$ represents activity of a radioactive sample. Then the activity of sample, varies with time according to the curve
A piece of wood from the ruins of an ancient building was found to have a $^{14}C$ activity of $12$ disintegrations per minute per gram of its carbon content. The $^{14}C$ activity of the living wood is $16$ disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of $^{14}C$ is $5760$ years.
Half life of $B{i^{210}}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left over after $10$ days is