Q. 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 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) $M^{0}LT^{2}$
B) $M^{0}L^{2}T^{- 4}$
C) $M^{0}LT^{- 3}$
D) $M^{0}L^{2}T^{- 1}$
Explanation
$\lbrack n\rbrack =$ Number of particles crossing a unit area in unit time=[$L^{- 2}T^{- 1}$] $\left\lbrack n_{2} \right\rbrack = \left\lbrack n_{1} \right\rbrack =$number of particles per unit volume = $\left\lbrack L^{- 3} \right\rbrack$ $\left\lbrack x_{2} \right\rbrack = \lbrack x_{1}\rbrack$ = positions $\therefore D = \frac{\lbrack n\rbrack\left\lbrack x_{2} - x_{1} \right\rbrack}{\left\lbrack n_{2} - n_{1} \right\rbrack} = \frac{\left\lbrack L^{- 2}T^{- 1} \right\rbrack \times \lbrack L\rbrack}{\lbrack L^{- 3}\rbrack} = \left\lfloor L^{2}T^{- 1} \right\rfloor$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.