Question

The number of particles crossing the unit area perpendicular to the x –axis per unit time, is given by:

$N=-D\left(\frac{n_2-n_1}{x_2-x_1}\right)$

Where

$n_1$ and $n_2$

are the numbers of particles per unit volume for the values of x meant to be $x_1$ and $x_2$ respectively. What is the dimensional formula for the diffusion constant D?

• A. $\left[M^{0}L{T}^2\right]$
• B. $\left[M^0{L}^2{T}^4\right]$
• C. $\left[M^{0}L{T}^{-3}\right]$
• D. $\left[M^0{L}^2{T}^{-1}\right]$

Answer 1

The correct option is D $\left[M^0{L}^2{T}^{-1}\right]$

$N=-D\left(\frac{n_2-n_1}{x_2-x_1}\right)\Rightarrow \left[M^0{L}^{-2}{T}^{-1}\right]=-D\left(\frac{M^0{L}^{-3}{T}^0}{M^0{L}^1{T}^0}\right)$
$\Rightarrow D=M^0{L}^2{T}^{-1}$