Q. The number of particles given by $n = - D\frac{n_{2} - n_{1}}{x_{2} - x_{1}}$ are 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 values $x_{1}$ and $x_{2}$ of $x$ respectively. Then the dimensional formula of diffusion constant $D$ is
A) [$M^{0}LT^{0}$]
B) [$M^{0}L^{2}T^{- 4}$]
C) [$M^{0}LT^{- 3}$]
D) [$M^{0}L^{2}T^{- 1}$]
Explanation
From the given relation, $D = - \frac{n(x_{2} - x_{1})}{n_{2}{- n}_{1}}$ Here [$n$]=$\left\lbrack \frac{1}{area \times time} \right\rbrack = \frac{1}{\lbrack L^{2}T\rbrack} = \lbrack L^{- 2}T^{- 1}\rbrack$ $x_{2} - x_{1} = \lbrack L\rbrack$ and $n_{2} - n_{1} = \left\lbrack \frac{1}{volume} \right\rbrack = \left\lbrack \frac{1}{L^{3}} \right\rbrack = \lbrack L^{- 3}\rbrack$ So, $\lbrack D\rbrack = \frac{\lbrack L^{- 2}T^{- 1}L\rbrack}{\lbrack L^{- 3}\rbrack} = \left\lbrack L^{2}T^{- 1} \right\rbrack.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.