Question

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

• 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

Answer: (D)

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

Given, number of particle passing from unit area in unit time $=n$

$=\frac{Numberofparticle}{A\times t}=\frac{\left[M^0{L}^0{T}^0\right]}{\left[L^2\right]\left[T\right]}=\left[L^{-2}{T}^{-1}\right]$

Now from the given formula $\left[D\right]=\frac{\left[n\right][x_2-x_1]}{[n_2-n_1]}=\left[L^2{T}^{-1}\right]$