$\left[ {{n_2}} \right] = \left[ {{n_1}} \right] $ = number of particles per unit volume $= [L-3]$

$ [{x_2}] = [{x_1}]$= positions  $D = \frac{{[n]\;\left[ {{x_2} - {x_1}} \right]}}{{\left[ {{n_2} - {n_1}} \right]}} = \frac{{\left[ {{L^{ - 2}}{T^{ - 1}}} \right] \times [L]}}{{[{L^{ - 3}}]}} $ $=\left[ {{L^2}{T^{ - 1}}} \right]$