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 $\quad n=-D\left[\frac{n_{2}-n_{1}}{x_{2}-x_{1}}ight]$ where $\quad n_{1}$ and $n_{2}$ are number of particles per unit volume at $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$. The dimensions of D 2233called diffusion constant are\

Professor PC Thomas Classes · Answer

$\mathrm{n}=-\mathrm{D} \frac{\mathrm{n}_{2}-\mathrm{n}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}$ 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 $n=L^{-2} T^{-1}$\ DF of $x_{2}-x_{1}=L$\ DF of $\mathrm{n}_{2}-\mathrm{n}_{1}=\mathrm{L}^{-3}$\ $\mathrm{D}=\frac{\mathrm{L}^{-2} \mathrm{~T}^{-1} 	imes \mathrm{L}}{\mathrm{L}^{-3}}=\mathrm{L}^{2} \mathrm{~T}^{-1}$\