Question

The number of particles is given by $n=-D\frac{n_2-n_1}{x_2-x_1}$ crossing a unit area perpendicular to X-axis in unit time, where $n_1$ and $n_2$ are the number of particles per unit volume for the value of $x$ meant to $x_2$ and $x_1$. Find the dimensions of $D$ called diffusion constant.

Answer 1

$N=$ no. of particle per unit area per unit time

$n_1$ & $n_2$ $=$ no. of particle per unit volume

$x_1$ & $x_2$ are distance from some reference point.

Dimension of ${}^{\prime }{N}^{\prime }=\left[L^{-2}{T}^{-1}\right]$

Dimensional formula of $n_1$ & $n_2$ $=\left[L^{-3}\right]$

Dimensional formula of $x_1$ & $x_2$ $=$ $\left[L\right]$

$N=-D\frac{n_2-n_1}{x_2-x_1}$

$D=-N\left[\frac{x_2-x_1}{n_2-n_1}\right]$

$=\frac{\left[L^{-2}{T}^{-1}\right]\left[L\right]}{\left[L^{-3}\right]}$

$D=\left[M^0{L}^2{T}^{-1}\right]$