Number of particles, given by n = - D n 2 - n 1 x 2 - x 1 , is crossing a unit area perpendicular to x -axis in unit time, where n 1 and n 2 are number of particles per unit volume for the value of x

Question

Number of particles, given by n = - D n 2 - n 1 x 2 - x 1 , is crossing a unit area perpendicular to x -axis in unit time, where n 1 and n 2 are number of particles per unit volume for the value of x meant to x 2 and x 1 . Find dimensions of D , called as diffusion constant.

TestHub · Accepted Answer

Given, number of particle passing from unit area in unit time $= n$

$= \frac{N u m b e r o f p a r t i c l e}{A \times t} = \frac{[M^{0} L^{0} T^{0}]}{[L^{2}] [T]} = [L^{- 2} T^{- 1}]$

$[n_{1}] = [n_{2}] = N u m b e r o f p a r t i c l e i n u n i t v o l u m e = [L^{- 3}]$

Now, from the given formula $[D] = \frac{[n] [x_{2} - x_{1}]}{[n_{2} - n_{1}]}$

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

$= [L^{2} T^{- 1}]$

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