Question

The no. of particles crossing a unit area perpendicular to X-axis in unit time us given by n=-D(n2-n1)/(x2-x1) where n1 and n2 are no. of particles per unit volume for the values of x meant to be x and x2. find the dimensions of the diffusion constant D

Answer 1

n is just number- every number is dimensionless. If you have on left side something dimensionless you should have something dimensionless on right side. the units change when you multiply or divide them by some units. They dont change when you add or substract them. Following that statements we get:
\[[\frac{ D(\frac{ 1 }{V }) }{ t }]\] must be dimensionless/ You can put some number( I've chosen 1 for "unit" of dimensionless) so this must be equal to 1. It's equal to 1 when D has unit of volume*time