State and explain Graham’s law of diffusion? Applications ?

“At constant temperature and pressure, the rate of diffusion of a gas inversely proportional to
the square root of its density”.
$\mathrm{r}\propto \frac{1}{\sqrt{\mathrm{d}}}\therefore \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}}$
The rate of diffusion of a gas is inversely proportional to square root of its molecular weight
$\mathrm{r}\propto \frac{1}{\sqrt{\mathrm{M}}}\therefore \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}}$
Molecular weight is the twice the vapour density
$\begin{array}{l}\mathrm{M}=2\times \mathrm{VD}\\ \therefore \frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}=\frac{{\mathrm{VD}}_1}{{\mathrm{VD}}_2}\Rightarrow \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}}=\sqrt{\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}}=\sqrt{\frac{{\mathrm{VD}}_2}{{\mathrm{VD}}_1}}\end{array}$
Applications :
1) It is used to separate Uranium isotopes by forming volatile hexa fluorides.
2) Working of ansil’s alarm in coal mines is based on diffusion.