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Byju's Answer

Standard XII

Physics

Dimensional Analysis

The number of...

Question

The number of particles crossing the unit area perpendicular to the x-axis per unit time is given by $N = - D (\frac{n_{2} - n_{1}}{x_{2} - x_{1}})$ when $n_{1}$ and $n_{2}$ are the numbers of particles per unit volume for the values of x meant to be $x_{1}$ and $x_{2}$ respectively. What is the dimensional formula for the diffusion constant D ?

M^{0} L T^{2}

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M^{0} L^{2} T^{4}

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M^{0} L T^{- 3}

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

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Solution

The correct option is D $M^{0} L^{2} T^{- 1}$
Since N is no. of particles per unit area per unit time, thus its dimensions are $m o l L^{- 2} T^{- 1}$ .
$n_{1}$ and $n_{2}$ are no. of particles per unit volume. Thus they have the dimensions $m o l L^{- 3}$ .
x has dimension of length, i.e $L$ .
Thus, D has dimensions of $\frac{N x}{n} = \frac{m o l L^{- 2} T^{- 1} L}{m o l L^{- 3}} = L^{2} T^{- 1}$

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