The number of particles crossing a unit area | vedclass

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Question

(D) The given formula is $n = -D \frac{n_2 - n_1}{x_2 - x_1}$.Here,$n$ represents the number of particles crossing a unit area in unit time,so its dim

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

Vedclass · Answer

(D) The given formula is $n = -D \frac{n_2 - n_1}{x_2 - x_1}$.Here,$n$ represents the number of particles crossing a unit area in unit time,so its dimensions are $[n] = [L^{-2} T^{-1}]$.$n_1$ and $n_2$ are the number of particles per unit volume,so their dimensions are $[n_1] = [n_2] = [L^{-3}]$.$x_1$ and $x_2$ are positions,so $[x_2 - x_1] = [L]$.Rearranging the formula for $D$,we get $D = n \frac{x_2 - x_1}{n_2 - n_1}$.Substituting the dimensions: $[D] = \frac{[L^{-2} T^{-1}] 	imes [L]}{[L^{-3}]}$.$[D] = \frac{[L^{-1} T^{-1}]}{[L^{-3}]} = [L^{-1+3} T^{-1}] = [L^2 T^{-1}]$.Thus,the dimensions of $D$ are $[M^0 L^2 T^{-1}]$.

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