The number of particles is given by $n = - D \frac{n_{2} - n_{1}}{x_{2} - x_{1}}$ crossing a unit area $⊥$ to X-axis in unit time, where n₁ and n₂, are number of particles per unit volume for the value of x₁, and x₂. Find dimensions of D called as diffusion constant

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M^oL²T^{- 4}

M^o LT²

M^o L² T^-1

M^oLT^-3

answer is D.

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Detailed Solution

Dimensional formula for $n = [L^{- 2} T^{- 1}]$
Dimensional formula of $n_{1} or n_{2} = [L^{- 3}]$
Now, $D = - n \frac{(x_{2} - x_{1})}{(n_{2} - n_{1})}$
or , $\begin{matrix} = \frac{[L^{- 2} T^{- 1}] [L]}{[L^{- 3}]} = [L^{2} T^{- 1}] \\ = [M^{0} L^{2} T^{- 1}] \end{matrix}$