The number of particles crossing a unit area perpendicular to the x-axis in a unit time is given by $n = - D (\frac{n_{2} - n_{1}}{x_{2} - x_{1}})$ , where n₁ and n₂ are the number of particles per unit volume at x = x₁ and x = x₂, respectively, and D is the diffusion constant. The dimensions of D are

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$[M^{0} {LT}^{- 2}]$

$[M^{0} L^{2} T^{- 4}]$

$[M^{0} L^{2} T^{- 2}]$

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

answer is D.

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Detailed Solution

$\begin{array}{l} n = - \frac{D (n_{2} - n_{1})}{x_{2} - x_{1}} \Rightarrow T^{- 1} L^{- 2} = \frac{D (L^{- 3})}{L} \Rightarrow D = \frac{T^{- 1} L^{- 2} \times L}{L^{- 3}} \\ \Rightarrow D = [M^{0} L^{2} T^{- 1}] \end{array}$

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