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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 $n_{1} a n d n_{2}$ are the number of particles per unit volume for the values $x_{1} a n d x_{2}$ of x respectively. Then the dimensional formula of diffusion constant D is

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

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

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

$[M^{0} L T^{- 3}]$

answer is D.

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Detailed Solution

From the given relation, $D = \frac{n (x_{2} - x_{1})}{n_{2} - n_{1}}$

Here, $[n] = [\frac{1}{a r e a \times t i m e}] = \frac{1}{[L^{2} T]} = [L^{- 2} T^{- 1}]$

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

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

So, $[D] = \frac{[L^{- 2} T^{- 1} L]}{[L^{- 3}]} = [L^{2} T^{- 1}]$

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