Draw a graph showing the variation of decay rate with number of active nuclei.
According to formula,
$\mathrm{I}=-\lambda \mathrm{N}$
$\therefore \mathrm{I}=(-\lambda) \mathrm{N}+0$
Form of above equation is like equation of a straight line, $y=m x+c .$ Hence graph of $\mathrm{I} \rightarrow \mathrm{N}$ is a straight line with slope $(-\lambda)$.
Here graph is obtained in $4^{\text {th }}$ quadrant because $N$ is positive and $I$ is negative.
At a given instant, say $t = 0,$ two radioactive substances $A$ and $B$ have equal activates. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activities. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activates after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is
$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half life of the element is
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 $ln\,\, 12 = 2.6)$
Unit of radioactivity is Rutherford. Its value is
A sample of radioactive element has a mass of $10\, gm$ at an instant $t = 0$.The approximate mass of this element in the sample after two mean lives is ..........$gm$