Question

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

• A. $L{T}^{-1}$
• B. $L^2{T}^{-1}$
• C. $LT$
• D. $L^{-1}T$

Answer 1

The correct option is B $L^2{T}^{-1}$

$N=-D\frac{(n_2-n_1)}{(x_2-x_1)}$
$N$ is the number of particles per unit area per unit time, so it has dimensions as $L^{-2}{T}^{-1}$.
$n_1,n_2$ are the number of particles per unit volume, so they have dimensions as $L^{-3}$.
Dimensions of $x_1,x_2$ are $M^0{L}^1{T}^0$.

Putting in equation and solving, $L^{-2}{T}^{-1}=\left[D\right]\times \frac{L^{-3}}{L}$
Thus we get dimensions of $D$ as $L^2{T}^{-1}$.