The number of particles $n$ crossing unit area perpendicular to $X$-axis in unit time is given by $\

Question

The number of particles $n$ crossing unit area perpendicular to $X$-axis in unit time is given by $\mathrm{n}=-\mathrm{D} \frac{\mathrm{n}_{2}-\mathrm{n}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}$ where $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ are number of particles per unit volume at $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$. The dimensions of D called diffusion constant are\

Professor PC Thomas Classes · Answer

$n=-D \frac{n_{2}-n_{1}}{x_{2}-x_{1}}$ Leave the -ve sign\ $\mathrm{D}=\frac{\mathrm{n}\left(\mathrm{x}_{2}-\mathrm{x}_{1}ight)}{\left(\mathrm{n}_{2}-\mathrm{n}_{1}ight)}$\ DF of $\mathrm{n}=\mathrm{L}^{-2} \mathrm{~T}^{-1}$\ DF of $\mathrm{x}_{2}-\mathrm{x}_{1}=\mathrm{L}$\ DF of $\mathrm{n}_{2}-\mathrm{n}_{1}=\mathrm{L}^{-3}$\ $\mathrm{D}=\frac{\mathrm{L}^{-2} \mathrm{~T}^{-1} 	imes \mathrm{L}}{\mathrm{L}^{-3}}$\ $=\mathrm{L}^{2} \mathrm{~T}^{-1}$\