Question

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

Answer 1

Answer: (D)

Given, number of particle passing from unit area in unit time $=n$
$=\frac{\text { Number of particle }}{A \times t}=\frac{\left[M^{0} L^{0} T^{0}\right]}{\left[L^{2}\right][T]}=\left[L^{-2} T^{-1}\right]$
$\left[n_{1}\right]=\left[n_{2}\right]=$ Number of particle in unit volume $=\left[L^{-3}\right]$
Now, from the given formula $[D]=\frac{[n]\left[x_{2}-x_{1}\right]}{\left[n_{2}-n_{1}\right]}$
$=\frac{\left[L^{-2} T^{-1}\right][L]}{\left[L^{-3}\right]} $
$=\left[L^{2} T^{-1}\right]$