The number of particles crossing the unit area normal to $x -$ axis per second is represented by the following formula $n = D \frac{n_{2} - n_{1}}{x_{2} - x_{1}}$ Where $D$ is the coefficient of diffusion and $n_{1}$ and $n_{2}$ are the number of molecules per unit volume at $x_{1}$ and $x_{2}$ respectively, then the dimensions of $D$ are

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

$M^{0} L T^{- 1}$

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

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

answer is A.

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Detailed Solution

$n = \frac{1}{a r e a \times t i m e} = \frac{1}{L^{2} T}$

$[n_{1} - n_{2}] = \frac{1}{V o l u m e} = \frac{1}{L^{3}}$

$[x_{2} - x_{1}] = L$

$\Rightarrow D = - \frac{n (x_{2} - x_{1})}{n_{2} - n_{1}} = \frac{L^{- 2} T^{- 1} L}{L^{- 3}} = L^{2} T^{- 1}$

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